--- OA_place: repository OA_type: green _id: '21140' abstract: - lang: eng text: 'We consider several problems related to packing forests in graphs. The first one is to find k edge-disjoint forests in a directed graph G of maximal size such that the indegree of each vertex in these forests is at most k. We describe a min-max characterization for this problem and show that it can be solved in almost linear time for fixed k, extending the algorithm of [Gabow, 1995]. Specifically, the complexity is O(kδm log n), where n, m are the number of vertices and edges in G respectively, and δ = max{1, k − kG}, where kG is the edge connectivity of the graph. Using our solution to this problem, we improve complexities for two existing applications:(1) k-forest problem: find k forests in an undirected graph G maximizing the number of edges in their union. We show how to solve this problem in O(k3 min{kn, m} log2 n + k · MAXFLOW(m, m) log n) time, breaking the Ok(n3/2) complexity barrier of previously known approaches.(2) Directed edge-connectivity augmentation problem: find a smallest set of directed edges whose addition to the given directed graph makes it strongly k-connected. We improve the deterministic complexity for this problem from O(kδ(m + δn) log n) [Gabow, STOC 1994] to O(kδm log n). A similar approach with the same complexity also works for the undirected version of the problem.' article_processing_charge: No arxiv: 1 author: - first_name: Pavel full_name: Arkhipov, Pavel id: b25f2ab2-1fed-11ee-8599-fe02d211784f last_name: Arkhipov - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Arkhipov P, Kolmogorov V. Faster algorithms for packing forests in graphs and related problems. In: Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2026:4023-4042. doi:10.1137/1.9781611978971.148' apa: 'Arkhipov, P., & Kolmogorov, V. (2026). Faster algorithms for packing forests in graphs and related problems. In Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 4023–4042). Vancouver, Canada: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611978971.148' chicago: Arkhipov, Pavel, and Vladimir Kolmogorov. “Faster Algorithms for Packing Forests in Graphs and Related Problems.” In Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, 4023–42. Society for Industrial and Applied Mathematics, 2026. https://doi.org/10.1137/1.9781611978971.148. ieee: P. Arkhipov and V. Kolmogorov, “Faster algorithms for packing forests in graphs and related problems,” in Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, Canada, 2026, pp. 4023–4042. ista: 'Arkhipov P, Kolmogorov V. 2026. Faster algorithms for packing forests in graphs and related problems. Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 4023–4042.' mla: Arkhipov, Pavel, and Vladimir Kolmogorov. “Faster Algorithms for Packing Forests in Graphs and Related Problems.” Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2026, pp. 4023–42, doi:10.1137/1.9781611978971.148. short: P. Arkhipov, V. Kolmogorov, in:, Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2026, pp. 4023–4042. conference: end_date: 2026-01-14 location: Vancouver, Canada name: 'SODA: Symposium on Discrete Algorithms' start_date: 2026-01-11 corr_author: '1' date_created: 2026-02-05T10:51:34Z date_published: 2026-01-07T00:00:00Z date_updated: 2026-02-16T09:18:33Z day: '07' department: - _id: VlKo doi: 10.1137/1.9781611978971.148 external_id: arxiv: - '2409.20314' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.20314 month: '01' oa: 1 oa_version: Preprint page: 4023-4042 publication: Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: eisbn: - '9781611978971' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' status: public title: Faster algorithms for packing forests in graphs and related problems type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2026' ... --- OA_place: repository _id: '21400' abstract: - lang: eng text: This document is a blueprint for the formalization in Lean of the structural theory of regular matroids underlying Seymour's decomposition theorem. We present a modular account of regularity via totally unimodular representations, show that regularity is preserved under 1-, 2-, and 3-sums, and establish regularity for several special classes of matroids, including graphic, cographic, and the matroid R10. The blueprint records the logical structure of the proof, the precise dependencies between results, and their correspondence with Lean declarations. It is intended both as a guide for the ongoing formalization effort and as a human-readable reference for the organization of the proof. article_processing_charge: No arxiv: 1 author: - first_name: Ivan full_name: Sergeev, Ivan id: ca3c9187-9a72-11ee-a009-8af825d896b0 last_name: Sergeev orcid: 0009-0004-9145-8785 - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Cameron full_name: Rampell, Cameron last_name: Rampell - first_name: Mark full_name: Sandey, Mark last_name: Sandey - first_name: Pietro full_name: Monticone, Pietro last_name: Monticone citation: ama: Sergeev I, Dvorak M, Rampell C, Sandey M, Monticone P. A blueprint for the formalization of Seymour’s matroid decomposition theorem. arXiv. doi:10.48550/arXiv.2601.01255 apa: Sergeev, I., Dvorak, M., Rampell, C., Sandey, M., & Monticone, P. (n.d.). A blueprint for the formalization of Seymour’s matroid decomposition theorem. arXiv. https://doi.org/10.48550/arXiv.2601.01255 chicago: Sergeev, Ivan, Martin Dvorak, Cameron Rampell, Mark Sandey, and Pietro Monticone. “A Blueprint for the Formalization of Seymour’s Matroid Decomposition Theorem.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2601.01255. ieee: I. Sergeev, M. Dvorak, C. Rampell, M. Sandey, and P. Monticone, “A blueprint for the formalization of Seymour’s matroid decomposition theorem,” arXiv. . ista: Sergeev I, Dvorak M, Rampell C, Sandey M, Monticone P. A blueprint for the formalization of Seymour’s matroid decomposition theorem. arXiv, 10.48550/arXiv.2601.01255. mla: Sergeev, Ivan, et al. “A Blueprint for the Formalization of Seymour’s Matroid Decomposition Theorem.” ArXiv, doi:10.48550/arXiv.2601.01255. short: I. Sergeev, M. Dvorak, C. Rampell, M. Sandey, P. Monticone, ArXiv (n.d.). corr_author: '1' date_created: 2026-03-04T12:09:26Z date_published: 2026-01-03T00:00:00Z date_updated: 2026-03-09T15:14:18Z day: '03' department: - _id: GradSch - _id: VlKo doi: 10.48550/arXiv.2601.01255 external_id: arxiv: - '2601.01255' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2601.01255 month: '01' oa: 1 oa_version: Preprint page: '18' publication: arXiv publication_status: submitted related_material: link: - relation: supplementary_material url: https://ivan-sergeyev.github.io/seymour/blueprint.pdf status: public title: A blueprint for the formalization of Seymour's matroid decomposition theorem tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2026' ... --- OA_place: repository _id: '21393' abstract: - lang: eng text: "This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer Science). The aim is to create code that is understandable, believable, useful, and elegant. The code should stand for itself as much as possible without a need for documentation; however, this text redundantly documents our code artifacts and provides additional context that isn’t present in the code. This thesis is written for readers who know Lean 4 but are not familiar with any of the topics presented. We manifest truth and beauty in three formalized areas of MathematiCS.\r\n\r\nWe formalize general grammars in Lean 4 and use grammars to show closure of the class of type-0 languages under four operations; union, reversal, concatenation, and the Kleene star.\r\n\r\nOur second stop is the theory of optimization. Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take “infinite values”. Additionally, we develop the basics of the theory of optimization in terms of the framework called General-Valued Constraint Satisfaction Problems, and we prove that, if a Rational-Valued Constraint Satisfaction Problem template has symmetric fractional polymorphisms of all arities, then its basic LP relaxation is tight.\r\n\r\nOur third stop is matroid theory. Seymour’s decomposition theorem is a hallmark result in matroid theory, presenting a structural characterization of the class of regular matroids. We aim to formally verify Seymour’s theorem in Lean 4. First, we build a library for working with totally unimodular matrices. We define binary matroids and their standard representations, and we prove that they form a matroid in the sense how Mathlib defines matroids. We define regular matroids to be matroids for which there exists a full representation rational matrix that is totally unimodular, and we prove that all regular matroids are binary. We define 1-sum, 2-sum, and 3 sum of binary matroids as specific ways to compose their standard representation matrices. We prove that the 1-sum, the 2-sum, and the 3-sum of regular matroids are a regular matroid, which concludes the composition direction of the Seymour’s theorem. The (more difficult) decomposition direction remains unproved.\r\n\r\nIn the pursuit of truth, we focus on identifying the trusted code in each project and presenting it faithfully. We emphasize the readability and believability of definitions rather than choosing definitions that are easier to work with. In search for beauty, we focus on the philosophical framework of Roger Scruton, who emphasizes that beauty is not a mere decoration but, most importantly, beauty is the means for shaping our place in the world and a source of redemption, where it can be viewed as a substitute for religion." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X citation: ama: 'Dvorak M. Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids. 2026. doi:10.15479/AT-ISTA-21393' apa: 'Dvorak, M. (2026). Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-21393' chicago: 'Dvorak, Martin. “Pursuit of Truth and Beauty in Lean 4 : Formally Verified Theory of Grammars, Optimization, Matroids.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-21393.' ieee: 'M. Dvorak, “Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids,” Institute of Science and Technology Austria, 2026.' ista: 'Dvorak M. 2026. Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids. Institute of Science and Technology Austria.' mla: 'Dvorak, Martin. Pursuit of Truth and Beauty in Lean 4 : Formally Verified Theory of Grammars, Optimization, Matroids. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-21393.' short: 'M. Dvorak, Pursuit of Truth and Beauty in Lean 4 : Formally Verified Theory of Grammars, Optimization, Matroids, Institute of Science and Technology Austria, 2026.' corr_author: '1' date_created: 2026-03-04T09:26:46Z date_published: 2026-03-04T00:00:00Z date_updated: 2026-03-27T12:37:00Z day: '04' ddc: - '511' - '000' degree_awarded: PhD department: - _id: GradSch - _id: VlKo doi: 10.15479/AT-ISTA-21393 file: - access_level: open_access checksum: cface6dc18152680962b5361575f6e4f content_type: application/pdf creator: mdvorak date_created: 2026-03-04T08:56:15Z date_updated: 2026-03-04T08:56:15Z file_id: '21394' file_name: 2026_Dvorak_Martin_Thesis.pdf file_size: 1771231 relation: main_file success: 1 - access_level: closed checksum: 290ddfacfb7e07fb07e6f0b334e67c90 content_type: application/vnd.openxmlformats-officedocument.wordprocessingml.document creator: mdvorak date_created: 2026-03-04T09:03:37Z date_updated: 2026-03-04T09:03:37Z file_id: '21395' file_name: 2026_Dvorak_Martin_Thesis.docx file_size: 864585 relation: source_file file_date_updated: 2026-03-04T09:03:37Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '160' publication_identifier: isbn: - 978-3-99078-074-9 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: link: - description: Full version of all definitions, statements, and proofs for Chapter 3.1 (Linear duality) relation: software url: https://github.com/madvorak/duality/tree/v3.5.0 - description: Full version of all definitions, statements, and proofs for Chapter 3.2 (Valued Constraint Satisfaction Problems) relation: software url: https://github.com/madvorak/vcsp/tree/v8.2.0 - description: Full version of all definitions, statements, and proofs for Chapter 4 (Seymour project) relation: software url: https://github.com/Ivan-Sergeyev/seymour/tree/v1.2.0 - description: Full version of all definitions, statements, and proofs for Chapter 5 (Theory of grammars) relation: software url: https://github.com/madvorak/chomsky/tree/v1.2.0 - description: Old version (Lean 3) of the project about grammars relation: software url: https://github.com/madvorak/grammars - description: Demonstration of (minimal) requirements for selected algebraic classes used in my Ph.D. thesis relation: software url: https://github.com/madvorak/preliminaries/blob/main/Preliminaries.lean record: - id: '13120' relation: part_of_dissertation status: public - id: '21398' relation: part_of_dissertation status: public - id: '20071' relation: part_of_dissertation status: public status: public supervisor: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Jasmin full_name: Blanchette, Jasmin last_name: Blanchette title: 'Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2026' ... --- OA_place: repository OA_type: green _id: '18855' abstract: - lang: eng text: "A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n]. Two important parameters are the partition function, which is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the vector of pre-image counts c_x=|H^-1(x)|.\r\nWe develop black-box sampling algorithms to estimate the counts roughly Õ(n²/ε²) samples for integer-valued distributions and Õ(q/ε²) samples for general distributions, where q = (log Z(β_max))/Z(β_min) \ (ignoring some second-order terms and parameters). We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs, independent sets, and perfect matchings. As a key subroutine, we estimate all values of the partition function using Õ(n²/ε²) samples for integer-valued distributions and Õ(q/ε²) samples for general distributions. This improves over a prior algorithm of Huber (2015) which computes a single point estimate Z(β_max) and which uses a slightly larger amount of samples. We show matching lower bounds, demonstrating this complexity is optimal as a function of n and q up to logarithmic terms." acknowledgement: "We thank Heng Guo for helpful explanations of algorithms for sampling connected subgraphs and matchings, and Maksym Serbyn for bringing to our attention the WL algorithm and its use in physics.\r\nThis is an extended version, which includes work under the same name from ICALP 2023, as well as the earlier work [22] appearing in COLT 2018.\r\nV. Kolmogorov was supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160" article_number: '3' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: David G. full_name: Harris, David G. last_name: Harris - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. ACM Transactions on Algorithms. 2025;21(1). doi:10.1145/3685676 apa: Harris, D. G., & Kolmogorov, V. (2025). Parameter estimation for Gibbs distributions. ACM Transactions on Algorithms. Association for Computing Machinery. https://doi.org/10.1145/3685676 chicago: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” ACM Transactions on Algorithms. Association for Computing Machinery, 2025. https://doi.org/10.1145/3685676. ieee: D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,” ACM Transactions on Algorithms, vol. 21, no. 1. Association for Computing Machinery, 2025. ista: Harris DG, Kolmogorov V. 2025. Parameter estimation for Gibbs distributions. ACM Transactions on Algorithms. 21(1), 3. mla: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” ACM Transactions on Algorithms, vol. 21, no. 1, 3, Association for Computing Machinery, 2025, doi:10.1145/3685676. short: D.G. Harris, V. Kolmogorov, ACM Transactions on Algorithms 21 (2025). corr_author: '1' date_created: 2025-01-19T23:01:52Z date_published: 2025-01-01T00:00:00Z date_updated: 2025-07-10T11:50:44Z day: '01' department: - _id: VlKo doi: 10.1145/3685676 ec_funded: 1 external_id: arxiv: - '2007.10824' isi: - '001399998600008' intvolume: ' 21' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2007.10824 month: '01' oa: 1 oa_version: Preprint project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: ACM Transactions on Algorithms publication_identifier: eissn: - 1549-6333 issn: - 1549-6325 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' related_material: record: - id: '14084' relation: earlier_version status: public scopus_import: '1' status: public title: Parameter estimation for Gibbs distributions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '10045' abstract: - lang: eng text: "Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n" acknowledgement: We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 2025;209:279-322. doi:10.1007/s10107-024-02064-5 apa: Dvorak, M., & Kolmogorov, V. (2025). Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02064-5 chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming. Springer Nature, 2025. https://doi.org/10.1007/s10107-024-02064-5. ieee: M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and discrete convexity,” Mathematical Programming, vol. 209. Springer Nature, pp. 279–322, 2025. ista: Dvorak M, Kolmogorov V. 2025. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 209, 279–322. mla: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming, vol. 209, Springer Nature, 2025, pp. 279–322, doi:10.1007/s10107-024-02064-5. short: M. Dvorak, V. Kolmogorov, Mathematical Programming 209 (2025) 279–322. corr_author: '1' date_created: 2021-09-27T10:48:23Z date_published: 2025-01-01T00:00:00Z date_updated: 2025-05-19T13:52:10Z day: '01' ddc: - '004' department: - _id: GradSch - _id: VlKo doi: 10.1007/s10107-024-02064-5 external_id: arxiv: - '2109.10203' isi: - '001176563300001' file: - access_level: open_access checksum: 25d9bd490719b45eca84f4d93a06c69f content_type: application/pdf creator: dernst date_created: 2025-04-16T09:36:08Z date_updated: 2025-04-16T09:36:08Z file_id: '19578' file_name: 2025_MathProgramming_Dvorak.pdf file_size: 839510 relation: main_file success: 1 file_date_updated: 2025-04-16T09:36:08Z has_accepted_license: '1' intvolume: ' 209' isi: 1 keyword: - minimum 0-extension problem - metric labeling problem - discrete metric spaces - metric extensions - computational complexity - valued constraint satisfaction problems - discrete convex analysis - L-convex functions language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 279-322 publication: Mathematical Programming publication_identifier: eissn: - 1436-4646 issn: - 0025-5610 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Generalized minimum 0-extension problem and discrete convexity tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 209 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '21007' abstract: - lang: eng text: 'Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes O(√(log n)/ε)-approximation using O(nε logO(1) n) maxflows for any ε∈[Θ(1/log n),Θ(1)]. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, JACM 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain "chaining" algorithm that combines results of multiple calls to the maxflow algorithm. We present an alternative approach that avoids solving the multicommodity flow problem and instead computes "violating paths". This simplifies Sherman''s algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute O(√(log n)/ε)-approximation via O(logO(1) n) maxflows using O(nε) processors. We also revisit Sherman''s chaining algorithm, and present a simpler version together with a new analysis.' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Kolmogorov V. A simpler and parallelizable O(√log n)-approximation algorithm for SPARSEST CUT. ACM Transactions on Algorithms. 2025;21(4):1-22. doi:10.1145/3748723 apa: Kolmogorov, V. (2025). A simpler and parallelizable O(√log n)-approximation algorithm for SPARSEST CUT. ACM Transactions on Algorithms. Association for Computing Machinery. https://doi.org/10.1145/3748723 chicago: Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for SPARSEST CUT.” ACM Transactions on Algorithms. Association for Computing Machinery, 2025. https://doi.org/10.1145/3748723. ieee: V. Kolmogorov, “A simpler and parallelizable O(√log n)-approximation algorithm for SPARSEST CUT,” ACM Transactions on Algorithms, vol. 21, no. 4. Association for Computing Machinery, pp. 1–22, 2025. ista: Kolmogorov V. 2025. A simpler and parallelizable O(√log n)-approximation algorithm for SPARSEST CUT. ACM Transactions on Algorithms. 21(4), 1–22. mla: Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for SPARSEST CUT.” ACM Transactions on Algorithms, vol. 21, no. 4, Association for Computing Machinery, 2025, pp. 1–22, doi:10.1145/3748723. short: V. Kolmogorov, ACM Transactions on Algorithms 21 (2025) 1–22. corr_author: '1' date_created: 2026-01-20T10:04:02Z date_published: 2025-10-01T00:00:00Z date_updated: 2026-01-21T09:46:26Z day: '01' ddc: - '510' department: - _id: VlKo doi: 10.1145/3748723 external_id: arxiv: - '2307.00115' file: - access_level: open_access checksum: 4a80fdb1e3711b9a2768d2bb8f6d3b4e content_type: application/pdf creator: dernst date_created: 2026-01-21T09:38:09Z date_updated: 2026-01-21T09:38:09Z file_id: '21031' file_name: 2025_ACMToA_Kolmogorov.pdf file_size: 2208302 relation: main_file success: 1 file_date_updated: 2026-01-21T09:38:09Z has_accepted_license: '1' intvolume: ' 21' issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1-22 publication: ACM Transactions on Algorithms publication_identifier: eissn: - 1549-6333 issn: - 1549-6325 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' related_material: record: - id: '17236' relation: shorter_version status: public scopus_import: '1' status: public title: A simpler and parallelizable O(√log n)-approximation algorithm for SPARSEST CUT tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2025' ... --- OA_place: publisher OA_type: diamond PlanS_conform: '1' _id: '21143' abstract: - lang: eng text: "The Lovász Local Lemma (LLL) is a powerful tool in probabilistic\r\ncombinatorics which can be used to establish the existence of objects with certain\r\nproperties. The breakthrough paper by Moser & Tardos (STOC’09 and JACM 2010)\r\nand follow-up work revealed that the LLL has intimate connections with a class of\r\nstochastic local search algorithms for finding such desirable objects.\r\nBesides conditions for convergence, many other natural questions can be asked\r\nabout algorithms; for instance, “are they parallelizable?”, “how many solutions can\r\nthey output?”, “what is the expected ‘weight’ of a solution?”. These questions and\r\nmore have been answered for a class of LLL-inspired algorithms called commutative. In\r\nthis paper we introduce a new, very natural and more general notion of commutativity\r\n(essentially matrix commutativity) which allows us to show a number of new refined\r\nproperties of LLL-inspired local search algorithms with significantly simpler proofs." acknowledgement: "This material is based on work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328. Supported by the European Research Council under the European Union’s Seventh Framework Programme\r\n(FP7/2007-2013)/ERC grant agreement no 616160." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: David G. full_name: Harris, David G. last_name: Harris - first_name: Fotios full_name: Iliopoulos, Fotios last_name: Iliopoulos - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. Theory of Computing. 2025;21(5):1-34. doi:10.4086/toc.2025.v021a005 apa: Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2025). A new notion of commutativity for the algorithmic Lovász Local Lemma. Theory of Computing. University of Chicago Press. https://doi.org/10.4086/toc.2025.v021a005 chicago: Harris, David G., Fotios Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Theory of Computing. University of Chicago Press, 2025. https://doi.org/10.4086/toc.2025.v021a005. ieee: D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” Theory of Computing, vol. 21, no. 5. University of Chicago Press, pp. 1–34, 2025. ista: Harris DG, Iliopoulos F, Kolmogorov V. 2025. A new notion of commutativity for the algorithmic Lovász Local Lemma. Theory of Computing. 21(5), 1–34. mla: Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Theory of Computing, vol. 21, no. 5, University of Chicago Press, 2025, pp. 1–34, doi:10.4086/toc.2025.v021a005. short: D.G. Harris, F. Iliopoulos, V. Kolmogorov, Theory of Computing 21 (2025) 1–34. corr_author: '1' date_created: 2026-02-05T12:04:58Z date_published: 2025-09-08T00:00:00Z date_updated: 2026-02-10T10:00:00Z day: '08' ddc: - '510' department: - _id: VlKo doi: 10.4086/toc.2025.v021a005 ec_funded: 1 external_id: arxiv: - '2008.05569' file: - access_level: open_access checksum: 5a9f7cfccac6046fe75a14a4059eed04 content_type: application/pdf creator: dernst date_created: 2026-02-10T09:54:28Z date_updated: 2026-02-10T09:54:28Z file_id: '21209' file_name: 2025_TheoryComputing_Harris.pdf file_size: 509346 relation: main_file success: 1 file_date_updated: 2026-02-10T09:54:28Z has_accepted_license: '1' intvolume: ' 21' issue: '5' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 1 - 34 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Theory of Computing publication_identifier: eissn: - 1557-2862 publication_status: published publisher: University of Chicago Press quality_controlled: '1' related_material: record: - id: '10072' relation: earlier_version status: public status: public title: A new notion of commutativity for the algorithmic Lovász Local Lemma tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2025' ... --- OA_place: repository OA_type: green _id: '21144' abstract: - lang: eng text: 'This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMIs). Since in some SDP instances all feasible solutions have irrational entries, numerical solvers that work with rational numbers can only find an approximate solution. We study the following question: Is it possible to certify feasibility of a given SDP using an approximate solution that is sufficiently close to some exact solution? Existing approaches make the assumption that there exist rational feasible solutions (and use techniques such as rounding and lattice reduction algorithms). We propose an alternative approach that does not need this assumption. More specifically, we show how to construct a system of polynomial equations whose set of real solutions is guaranteed to have an isolated correct solution (assuming that the target exact solution is maximum-rank). This allows, in particular, for us to use algorithms from real algebraic geometry for solving systems of polynomial equations, yielding a hybrid (or symbolic-numerical) method for SDPs. We experimentally compare it with a pure symbolic method in [D. Henrion, S. Naldi, and M. Safey El Din, SIAM J. Optim., 26 (2016), pp. 2512–2539]; the hybrid method was able to certify feasibility of many SDP instances on which the aforementioned paper failed. Our approach may have further applications, such as refining an approximate solution using methods of numerical algebraic geometry for systems of polynomial equations.' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Simone full_name: Naldi, Simone last_name: Naldi - first_name: Jeferson full_name: Zapata, Jeferson id: 00223538-AF8F-11E9-A4C7-F729E6697425 last_name: Zapata citation: ama: Kolmogorov V, Naldi S, Zapata J. Certifying solutions of degenerate semidefinite programs. SIAM Journal on Optimization. 2025;35(3):1630-1654. doi:10.1137/24m1664691 apa: Kolmogorov, V., Naldi, S., & Zapata, J. (2025). Certifying solutions of degenerate semidefinite programs. SIAM Journal on Optimization. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/24m1664691 chicago: Kolmogorov, Vladimir, Simone Naldi, and Jeferson Zapata. “Certifying Solutions of Degenerate Semidefinite Programs.” SIAM Journal on Optimization. Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/24m1664691. ieee: V. Kolmogorov, S. Naldi, and J. Zapata, “Certifying solutions of degenerate semidefinite programs,” SIAM Journal on Optimization, vol. 35, no. 3. Society for Industrial and Applied Mathematics, pp. 1630–1654, 2025. ista: Kolmogorov V, Naldi S, Zapata J. 2025. Certifying solutions of degenerate semidefinite programs. SIAM Journal on Optimization. 35(3), 1630–1654. mla: Kolmogorov, Vladimir, et al. “Certifying Solutions of Degenerate Semidefinite Programs.” SIAM Journal on Optimization, vol. 35, no. 3, Society for Industrial and Applied Mathematics, 2025, pp. 1630–54, doi:10.1137/24m1664691. short: V. Kolmogorov, S. Naldi, J. Zapata, SIAM Journal on Optimization 35 (2025) 1630–1654. date_created: 2026-02-05T13:33:05Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-02-16T11:52:23Z day: '01' department: - _id: VlKo - _id: GradSch doi: 10.1137/24m1664691 external_id: arxiv: - '2405.13625' intvolume: ' 35' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.13625 month: '09' oa: 1 oa_version: Preprint page: 1630-1654 publication: SIAM Journal on Optimization publication_identifier: eissn: - 1095-7189 issn: - 1052-6234 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' status: public title: Certifying solutions of degenerate semidefinite programs type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 35 year: '2025' ... --- OA_place: repository _id: '21399' abstract: - lang: eng text: We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas. article_processing_charge: No arxiv: 1 author: - first_name: Matthew full_name: Bolan, Matthew last_name: Bolan - first_name: Joachim full_name: Breitner, Joachim last_name: Breitner - first_name: Jose full_name: Brox, Jose last_name: Brox - first_name: Nicholas full_name: Carlini, Nicholas last_name: Carlini - first_name: Mario full_name: Carneiro, Mario last_name: Carneiro - first_name: Floris van full_name: Doorn, Floris van last_name: Doorn - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Andrés full_name: Goens, Andrés last_name: Goens - first_name: Aaron full_name: Hill, Aaron last_name: Hill - first_name: Harald full_name: Husum, Harald last_name: Husum - first_name: Hernán Ibarra full_name: Mejia, Hernán Ibarra last_name: Mejia - first_name: Zoltan A. full_name: Kocsis, Zoltan A. last_name: Kocsis - first_name: Bruno Le full_name: Floch, Bruno Le last_name: Floch - first_name: Amir full_name: Bar-on, Amir last_name: Bar-on - first_name: Lorenzo full_name: Luccioli, Lorenzo last_name: Luccioli - first_name: Douglas full_name: McNeil, Douglas last_name: McNeil - first_name: Alex full_name: Meiburg, Alex last_name: Meiburg - first_name: Pietro full_name: Monticone, Pietro last_name: Monticone - first_name: Pace P. full_name: Nielsen, Pace P. last_name: Nielsen - first_name: Emmanuel Osalotioman full_name: Osazuwa, Emmanuel Osalotioman last_name: Osazuwa - first_name: Giovanni full_name: Paolini, Giovanni last_name: Paolini - first_name: Marco full_name: Petracci, Marco last_name: Petracci - first_name: Bernhard full_name: Reinke, Bernhard last_name: Reinke - first_name: David full_name: Renshaw, David last_name: Renshaw - first_name: Marcus full_name: Rossel, Marcus last_name: Rossel - first_name: Cody full_name: Roux, Cody last_name: Roux - first_name: Jérémy full_name: Scanvic, Jérémy last_name: Scanvic - first_name: Shreyas full_name: Srinivas, Shreyas last_name: Srinivas - first_name: Anand Rao full_name: Tadipatri, Anand Rao last_name: Tadipatri - first_name: Terence full_name: Tao, Terence last_name: Tao - first_name: Vlad full_name: Tsyrklevich, Vlad last_name: Tsyrklevich - first_name: Fernando full_name: Vaquerizo-Villar, Fernando last_name: Vaquerizo-Villar - first_name: Daniel full_name: Weber, Daniel last_name: Weber - first_name: Fan full_name: Zheng, Fan last_name: Zheng citation: ama: 'Bolan M, Breitner J, Brox J, et al. The equational theories project: Advancing collaborative mathematical research at scale. arXiv. doi:10.48550/arXiv.2512.07087' apa: 'Bolan, M., Breitner, J., Brox, J., Carlini, N., Carneiro, M., Doorn, F. van, … Zheng, F. (n.d.). The equational theories project: Advancing collaborative mathematical research at scale. arXiv. https://doi.org/10.48550/arXiv.2512.07087' chicago: 'Bolan, Matthew, Joachim Breitner, Jose Brox, Nicholas Carlini, Mario Carneiro, Floris van Doorn, Martin Dvorak, et al. “The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2512.07087.' ieee: 'M. Bolan et al., “The equational theories project: Advancing collaborative mathematical research at scale,” arXiv. .' ista: 'Bolan M, Breitner J, Brox J, Carlini N, Carneiro M, Doorn F van, Dvorak M, Goens A, Hill A, Husum H, Mejia HI, Kocsis ZA, Floch BL, Bar-on A, Luccioli L, McNeil D, Meiburg A, Monticone P, Nielsen PP, Osazuwa EO, Paolini G, Petracci M, Reinke B, Renshaw D, Rossel M, Roux C, Scanvic J, Srinivas S, Tadipatri AR, Tao T, Tsyrklevich V, Vaquerizo-Villar F, Weber D, Zheng F. The equational theories project: Advancing collaborative mathematical research at scale. arXiv, 10.48550/arXiv.2512.07087.' mla: 'Bolan, Matthew, et al. “The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale.” ArXiv, doi:10.48550/arXiv.2512.07087.' short: M. Bolan, J. Breitner, J. Brox, N. Carlini, M. Carneiro, F. van Doorn, M. Dvorak, A. Goens, A. Hill, H. Husum, H.I. Mejia, Z.A. Kocsis, B.L. Floch, A. Bar-on, L. Luccioli, D. McNeil, A. Meiburg, P. Monticone, P.P. Nielsen, E.O. Osazuwa, G. Paolini, M. Petracci, B. Reinke, D. Renshaw, M. Rossel, C. Roux, J. Scanvic, S. Srinivas, A.R. Tadipatri, T. Tao, V. Tsyrklevich, F. Vaquerizo-Villar, D. Weber, F. Zheng, ArXiv (n.d.). date_created: 2026-03-04T12:00:16Z date_published: 2025-12-16T00:00:00Z date_updated: 2026-03-12T08:36:21Z day: '16' department: - _id: GradSch - _id: VlKo doi: 10.48550/arXiv.2512.07087 external_id: arxiv: - '2512.07087' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2512.07087 month: '12' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted status: public title: 'The equational theories project: Advancing collaborative mathematical research at scale' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: repository _id: '21398' abstract: - lang: eng text: Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and results about totally unimodular matrices, vector matroids, their standard representations, regular matroids, and 1-, 2-, and 3-sums of matrices and binary matroids given by their standard representations. Using this framework, we formally state Seymour's decomposition theorem and implement a formally verified proof of the composition direction in the setting where the matroids have finite rank and may have infinite ground sets. acknowledgement: "We would like to dedicate the paper to the memory of Klaus Truemper, whose monograph Matroid Decomposition [12]\r\nlaid the foundation for our entire work." article_processing_charge: No arxiv: 1 author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Tristan full_name: Figueroa-Reid, Tristan last_name: Figueroa-Reid - first_name: Rida full_name: Hamadani, Rida last_name: Hamadani - first_name: Byung-Hak full_name: Hwang, Byung-Hak last_name: Hwang - first_name: Evgenia full_name: Karunus, Evgenia last_name: Karunus - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Alexander full_name: Meiburg, Alexander last_name: Meiburg - first_name: Alexander full_name: Nelson, Alexander last_name: Nelson - first_name: Peter full_name: Nelson, Peter last_name: Nelson - first_name: Mark full_name: Sandey, Mark last_name: Sandey - first_name: Ivan full_name: Sergeev, Ivan id: ca3c9187-9a72-11ee-a009-8af825d896b0 last_name: Sergeev orcid: 0009-0004-9145-8785 citation: ama: Dvorak M, Figueroa-Reid T, Hamadani R, et al. Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv. doi:10.48550/arXiv.2509.20539 apa: Dvorak, M., Figueroa-Reid, T., Hamadani, R., Hwang, B.-H., Karunus, E., Kolmogorov, V., … Sergeev, I. (n.d.). Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv. https://doi.org/10.48550/arXiv.2509.20539 chicago: Dvorak, Martin, Tristan Figueroa-Reid, Rida Hamadani, Byung-Hak Hwang, Evgenia Karunus, Vladimir Kolmogorov, Alexander Meiburg, et al. “Composition Direction of Seymour’s Theorem for Regular Matroids — Formally Verified.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2509.20539. ieee: M. Dvorak et al., “Composition direction of Seymour’s theorem for regular matroids — Formally verified,” arXiv. . ista: Dvorak M, Figueroa-Reid T, Hamadani R, Hwang B-H, Karunus E, Kolmogorov V, Meiburg A, Nelson A, Nelson P, Sandey M, Sergeev I. Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv, 10.48550/arXiv.2509.20539. mla: Dvorak, Martin, et al. “Composition Direction of Seymour’s Theorem for Regular Matroids — Formally Verified.” ArXiv, doi:10.48550/arXiv.2509.20539. short: M. Dvorak, T. Figueroa-Reid, R. Hamadani, B.-H. Hwang, E. Karunus, V. Kolmogorov, A. Meiburg, A. Nelson, P. Nelson, M. Sandey, I. Sergeev, ArXiv (n.d.). corr_author: '1' date_created: 2026-03-04T11:56:29Z date_published: 2025-09-23T00:00:00Z date_updated: 2026-03-27T12:36:59Z day: '23' department: - _id: GradSch - _id: VlKo doi: 10.48550/arXiv.2509.20539 external_id: arxiv: - '2509.20539' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2509.20539 month: '09' oa: 1 oa_version: Preprint page: '21' publication: arXiv publication_status: draft related_material: record: - id: '21393' relation: dissertation_contains status: public status: public title: Composition direction of Seymour's theorem for regular matroids — Formally verified type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '17236' abstract: - lang: eng text: "Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes O(√(log n)/ε)-approximation using O(nε logO(1) n) maxflows for any ε∈[Θ(1/log n),Θ(1)]. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, JACM 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain \"chaining\" algorithm that combines results of multiple calls to the maxflow algorithm.\r\nWe present an alternative approach that avoids solving the multicommodity flow problem and instead computes \"violating paths\". This simplifies Sherman's algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute O(√(log n)/ε)-approximation via O(logO(1) n) maxflows using O(nε) processors.\r\nWe also revisit Sherman's chaining algorithm, and present a simpler version together with a new analysis." article_processing_charge: Yes (via OA deal) arxiv: 1 author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Kolmogorov V. A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. In: Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures. Association for Computing Machinery; 2024:403-414. doi:10.1145/3626183.3659969' apa: 'Kolmogorov, V. (2024). A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. In Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures (pp. 403–414). Nantes, France: Association for Computing Machinery. https://doi.org/10.1145/3626183.3659969' chicago: Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for Sparsest Cut.” In Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, 403–14. Association for Computing Machinery, 2024. https://doi.org/10.1145/3626183.3659969. ieee: V. Kolmogorov, “A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut,” in Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Nantes, France, 2024, pp. 403–414. ista: 'Kolmogorov V. 2024. A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures. SPAA: Symposium on Parallelism in Algorithms and Architectures, 403–414.' mla: Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for Sparsest Cut.” Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2024, pp. 403–14, doi:10.1145/3626183.3659969. short: V. Kolmogorov, in:, Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2024, pp. 403–414. conference: end_date: 2024-06-21 location: Nantes, France name: 'SPAA: Symposium on Parallelism in Algorithms and Architectures' start_date: 2024-06-17 corr_author: '1' date_created: 2024-07-14T22:01:11Z date_published: 2024-06-17T00:00:00Z date_updated: 2026-01-21T09:46:25Z day: '17' ddc: - '510' department: - _id: VlKo doi: 10.1145/3626183.3659969 external_id: arxiv: - '2307.00115' isi: - '001253331900044' file: - access_level: open_access checksum: 6ca18ac8508719dbd5d5735f4c991af2 content_type: application/pdf creator: dernst date_created: 2024-07-16T06:38:08Z date_updated: 2024-07-16T06:38:08Z file_id: '17245' file_name: 2024_SPAA_Kolmogorov.pdf file_size: 1116166 relation: main_file success: 1 file_date_updated: 2024-07-16T06:38:08Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 403-414 publication: Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures publication_identifier: isbn: - '9798400704161' issn: - 1548-6109 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' related_material: record: - id: '21007' relation: extended_version status: public scopus_import: '1' status: public title: A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- OA_place: repository OA_type: green _id: '20071' abstract: - lang: eng text: Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take "infinite values". acknowledgement: We would like to thank David Bartl and Jasmin Blanchette for frequent consultations. We would also like to express gratitude to Andrew Yang for the proof of Finset.univ sum of zero when not and to Henrik B¨oving for a help with generalization from extended rationals to extended linearly ordered fields. We would also like to acknowledge Antoine Chambert-Loir, Apurva Nakade, Ya¨el Dillies, Richard Copley, Edward van de Meent, Markus Himmel, Mario Carneiro, and Kevin Buzzard. article_number: '2409.08119' article_processing_charge: No arxiv: 1 author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally  verified. arXiv. doi:10.48550/arXiv.2409.08119 apa: Dvorak, M., & Kolmogorov, V. (n.d.). Duality theory in linear optimization and its extensions -- formally  verified. arXiv. https://doi.org/10.48550/arXiv.2409.08119 chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally  Verified.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.08119. ieee: M. Dvorak and V. Kolmogorov, “Duality theory in linear optimization and its extensions -- formally  verified,” arXiv. . ista: Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally  verified. arXiv, 2409.08119. mla: Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally  Verified.” ArXiv, 2409.08119, doi:10.48550/arXiv.2409.08119. short: M. Dvorak, V. Kolmogorov, ArXiv (n.d.). corr_author: '1' date_created: 2025-07-23T11:21:52Z date_published: 2024-09-12T00:00:00Z date_updated: 2026-03-27T12:36:59Z day: '12' department: - _id: GradSch - _id: VlKo doi: 10.48550/arXiv.2409.08119 external_id: arxiv: - '2409.08119' keyword: - Farkas lemma - linear programming - extended reals - calculus of inductive constructions language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.08119 month: '09' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: link: - description: full version of all definitions, statement, and proofs relation: software url: https://github.com/madvorak/duality/tree/v3.2 record: - id: '21393' relation: dissertation_contains status: public status: public title: Duality theory in linear optimization and its extensions -- formally verified type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- _id: '14084' abstract: - lang: eng text: "A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We will consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²) samples for integer-valued distributions (ignoring some second-order terms and parameters), We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph." acknowledgement: We thank Heng Guo for helpful explanations of algorithms for sampling connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the Wang-Landau algorithm and its use in physics. alternative_title: - LIPIcs article_number: '72' article_processing_charge: Yes arxiv: 1 author: - first_name: David G. full_name: Harris, David G. last_name: Harris - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In: 50th International Colloquium on Automata, Languages, and Programming. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.72' apa: 'Harris, D. G., & Kolmogorov, V. (2023). Parameter estimation for Gibbs distributions. In 50th International Colloquium on Automata, Languages, and Programming (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.72' chicago: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” In 50th International Colloquium on Automata, Languages, and Programming, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.72. ieee: D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,” in 50th International Colloquium on Automata, Languages, and Programming, Paderborn, Germany, 2023, vol. 261. ista: 'Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions. 50th International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming, LIPIcs, vol. 261, 72.' mla: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” 50th International Colloquium on Automata, Languages, and Programming, vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ICALP.2023.72. short: D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. conference: end_date: 2023-07-14 location: Paderborn, Germany name: 'ICALP: Automata, Languages and Programming' start_date: 2023-07-10 corr_author: '1' date_created: 2023-08-20T22:01:14Z date_published: 2023-07-01T00:00:00Z date_updated: 2025-07-10T11:50:45Z day: '01' ddc: - '000' - '510' department: - _id: VlKo doi: 10.4230/LIPIcs.ICALP.2023.72 external_id: arxiv: - '2007.10824' file: - access_level: open_access checksum: 6dee0684245bb1c524b9c955db1e933d content_type: application/pdf creator: dernst date_created: 2023-08-21T06:45:16Z date_updated: 2023-08-21T06:45:16Z file_id: '14088' file_name: 2023_LIPIcsICALP_Harris.pdf file_size: 917791 relation: main_file success: 1 file_date_updated: 2023-08-21T06:45:16Z has_accepted_license: '1' intvolume: ' 261' language: - iso: eng month: '07' oa: 1 oa_version: Published Version publication: 50th International Colloquium on Automata, Languages, and Programming publication_identifier: isbn: - '9783959772785' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '18855' relation: later_version status: public scopus_import: '1' status: public title: Parameter estimation for Gibbs distributions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 261 year: '2023' ... --- _id: '14448' abstract: - lang: eng text: We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in [16], [35]. As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subroutine based on in-face Frank-Wolfe directions, introduced in [4] in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html. article_processing_charge: No arxiv: 1 author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Kolmogorov V. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol 2023. IEEE; 2023:11980-11989. doi:10.1109/CVPR52729.2023.01153' apa: 'Kolmogorov, V. (2023). Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 2023, pp. 11980–11989). Vancouver, Canada: IEEE. https://doi.org/10.1109/CVPR52729.2023.01153' chicago: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2023:11980–89. IEEE, 2023. https://doi.org/10.1109/CVPR52729.2023.01153.' ieee: 'V. Kolmogorov, “Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vancouver, Canada, 2023, vol. 2023, pp. 11980–11989.' ista: 'Kolmogorov V. 2023. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2023, 11980–11989.' mla: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2023, IEEE, 2023, pp. 11980–89, doi:10.1109/CVPR52729.2023.01153.' short: V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2023, pp. 11980–11989. conference: end_date: 2023-06-24 location: Vancouver, Canada name: 'CVPR: Conference on Computer Vision and Pattern Recognition' start_date: 2023-06-17 corr_author: '1' date_created: 2023-10-22T22:01:16Z date_published: 2023-08-22T00:00:00Z date_updated: 2025-09-09T13:09:58Z day: '22' department: - _id: VlKo doi: 10.1109/CVPR52729.2023.01153 external_id: arxiv: - '2010.09567' isi: - '001062522104029' intvolume: ' 2023' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2010.09567' month: '08' oa: 1 oa_version: Preprint page: 11980-11989 publication: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition publication_identifier: isbn: - '9798350301298' issn: - 1063-6919 publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: 'Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions' type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2023 year: '2023' ... --- _id: '13120' abstract: - lang: eng text: 'We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant. We defined basic notions of rewrite rules and of words derived by a grammar, and used grammars to show closure of the class of type-0 languages under four operations: union, reversal, concatenation, and the Kleene star. The literature mostly focuses on Turing machine arguments, which are possibly more difficult to formalize. For the Kleene star, we could not follow the literature and came up with our own grammar-based construction.' acknowledgement: "Jasmin Blanchette: This research has received funding from the Netherlands Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No. 016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making this collaboration possible. We\r\nthank Václav Končický for discussing ideas about the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano Testa for their small yet very valuable contributions to our code. We thank Eric Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting textual improvements. We thank the anonymous reviewers for very helpful comments. Finally, we thank the Lean community for helping us with various technical issues and answering many questions. " alternative_title: - LIPIcs article_number: '15' article_processing_charge: No arxiv: 1 author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Jasmin full_name: Blanchette, Jasmin last_name: Blanchette citation: ama: 'Dvorak M, Blanchette J. Closure properties of general grammars - formally verified. In: 14th International Conference on Interactive Theorem Proving. Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ITP.2023.15' apa: 'Dvorak, M., & Blanchette, J. (2023). Closure properties of general grammars - formally verified. In 14th International Conference on Interactive Theorem Proving (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ITP.2023.15' chicago: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” In 14th International Conference on Interactive Theorem Proving, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ITP.2023.15. ieee: M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally verified,” in 14th International Conference on Interactive Theorem Proving, Bialystok, Poland, 2023, vol. 268. ista: 'Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally verified. 14th International Conference on Interactive Theorem Proving. ITP: Interactive Theorem Proving, LIPIcs, vol. 268, 15.' mla: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” 14th International Conference on Interactive Theorem Proving, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ITP.2023.15. short: M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. conference: end_date: 2023-08-04 location: Bialystok, Poland name: 'ITP: Interactive Theorem Proving' start_date: 2023-07-31 corr_author: '1' date_created: 2023-06-05T07:29:05Z date_published: 2023-07-27T00:00:00Z date_updated: 2026-03-27T12:36:59Z day: '27' ddc: - '000' department: - _id: GradSch - _id: VlKo doi: 10.4230/LIPIcs.ITP.2023.15 external_id: arxiv: - '2302.06420' isi: - '001515590500015' file: - access_level: open_access checksum: 773a0197f05b67feaa6cb1e17ec3642d content_type: application/pdf creator: dernst date_created: 2023-08-07T11:55:43Z date_updated: 2023-08-07T11:55:43Z file_id: '13982' file_name: 2023_LIPIcS_Dvorak.pdf file_size: 715976 relation: main_file success: 1 file_date_updated: 2023-08-07T11:55:43Z has_accepted_license: '1' intvolume: ' 268' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version publication: 14th International Conference on Interactive Theorem Proving publication_identifier: eissn: - 1868-8969 isbn: - '9783959772846' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: link: - relation: software url: https://github.com/madvorak/grammars/tree/publish record: - id: '21393' relation: dissertation_contains status: public scopus_import: '1' status: public title: Closure properties of general grammars - formally verified tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 268 year: '2023' ... --- _id: '10737' abstract: - lang: eng text: We consider two models for the sequence labeling (tagging) problem. The first one is a Pattern-Based Conditional Random Field (PB), in which the energy of a string (chain labeling) x=x1⁢…⁢xn∈Dn is a sum of terms over intervals [i,j] where each term is non-zero only if the substring xi⁢…⁢xj equals a prespecified word w∈Λ. The second model is a Weighted Context-Free Grammar (WCFG) frequently used for natural language processing. PB and WCFG encode local and non-local interactions respectively, and thus can be viewed as complementary. We propose a Grammatical Pattern-Based CRF model (GPB) that combines the two in a natural way. We argue that it has certain advantages over existing approaches such as the Hybrid model of Benedí and Sanchez that combines N-grams and WCFGs. The focus of this paper is to analyze the complexity of inference tasks in a GPB such as computing MAP. We present a polynomial-time algorithm for general GPBs and a faster version for a special case that we call Interaction Grammars. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Rustem full_name: Takhanov, Rustem id: 2CCAC26C-F248-11E8-B48F-1D18A9856A87 last_name: Takhanov - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Takhanov R, Kolmogorov V. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 2022;26(1):257-272. doi:10.3233/IDA-205623 apa: Takhanov, R., & Kolmogorov, V. (2022). Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. IOS Press. https://doi.org/10.3233/IDA-205623 chicago: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis. IOS Press, 2022. https://doi.org/10.3233/IDA-205623. ieee: R. Takhanov and V. Kolmogorov, “Combining pattern-based CRFs and weighted context-free grammars,” Intelligent Data Analysis, vol. 26, no. 1. IOS Press, pp. 257–272, 2022. ista: Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 26(1), 257–272. mla: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis, vol. 26, no. 1, IOS Press, 2022, pp. 257–72, doi:10.3233/IDA-205623. short: R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 257–272. corr_author: '1' date_created: 2022-02-06T23:01:32Z date_published: 2022-01-14T00:00:00Z date_updated: 2024-10-09T21:01:33Z day: '14' department: - _id: VlKo doi: 10.3233/IDA-205623 external_id: arxiv: - '1404.5475' isi: - '000749997700015' intvolume: ' 26' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1404.5475 month: '01' oa: 1 oa_version: Preprint page: 257-272 publication: Intelligent Data Analysis publication_identifier: eissn: - 1571-4128 issn: - 1088-467X publication_status: published publisher: IOS Press quality_controlled: '1' scopus_import: '1' status: public title: Combining pattern-based CRFs and weighted context-free grammars type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2022' ... --- _id: '9365' abstract: - lang: eng text: In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method. acknowledgement: The second author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Ferdinard U. full_name: Ogbuisi, Ferdinard U. last_name: Ogbuisi - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Jen Chih full_name: Yao, Jen Chih last_name: Yao citation: ama: Ogbuisi FU, Shehu Y, Yao JC. Convergence analysis of new inertial method for the split common null point problem. Optimization. 2022;71(13):3767-3795. doi:10.1080/02331934.2021.1914035 apa: Ogbuisi, F. U., Shehu, Y., & Yao, J. C. (2022). Convergence analysis of new inertial method for the split common null point problem. Optimization. Taylor and Francis. https://doi.org/10.1080/02331934.2021.1914035 chicago: Ogbuisi, Ferdinard U., Yekini Shehu, and Jen Chih Yao. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization. Taylor and Francis, 2022. https://doi.org/10.1080/02331934.2021.1914035. ieee: F. U. Ogbuisi, Y. Shehu, and J. C. Yao, “Convergence analysis of new inertial method for the split common null point problem,” Optimization, vol. 71, no. 13. Taylor and Francis, pp. 3767–3795, 2022. ista: Ogbuisi FU, Shehu Y, Yao JC. 2022. Convergence analysis of new inertial method for the split common null point problem. Optimization. 71(13), 3767–3795. mla: Ogbuisi, Ferdinard U., et al. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization, vol. 71, no. 13, Taylor and Francis, 2022, pp. 3767–95, doi:10.1080/02331934.2021.1914035. short: F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization 71 (2022) 3767–3795. date_created: 2021-05-02T22:01:29Z date_published: 2022-11-01T00:00:00Z date_updated: 2024-11-04T13:52:36Z day: '01' department: - _id: VlKo doi: 10.1080/02331934.2021.1914035 ec_funded: 1 external_id: isi: - '000640109300001' intvolume: ' 71' isi: 1 issue: '13' language: - iso: eng month: '11' oa_version: None page: 3767-3795 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization publication_identifier: eissn: - 1029-4945 issn: - 0233-1934 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: Convergence analysis of new inertial method for the split common null point problem type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 71 year: '2022' ... --- _id: '9469' abstract: - lang: eng text: In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis. acknowledgement: The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Cyril D. full_name: Enyi, Cyril D. last_name: Enyi - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2022;37(4):1527-1565. doi:10.1080/10556788.2021.1924715 apa: Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2022). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715 chicago: Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor and Francis, 2022. https://doi.org/10.1080/10556788.2021.1924715. ieee: O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software, vol. 37, no. 4. Taylor and Francis, pp. 1527–1565, 2022. ista: Iyiola OS, Enyi CD, Shehu Y. 2022. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 37(4), 1527–1565. mla: Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, vol. 37, no. 4, Taylor and Francis, 2022, pp. 1527–65, doi:10.1080/10556788.2021.1924715. short: O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software 37 (2022) 1527–1565. corr_author: '1' date_created: 2021-06-06T22:01:30Z date_published: 2022-07-01T00:00:00Z date_updated: 2024-11-04T13:52:36Z day: '01' department: - _id: VlKo doi: 10.1080/10556788.2021.1924715 ec_funded: 1 external_id: isi: - '000650507600001' intvolume: ' 37' isi: 1 issue: '4' language: - iso: eng month: '07' oa_version: None page: 1527-1565 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization Methods and Software publication_identifier: eissn: - 1029-4937 issn: - 1055-6788 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: Reflected three-operator splitting method for monotone inclusion problem type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 37 year: '2022' ... --- _id: '7577' abstract: - lang: eng text: Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods. acknowledgement: The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola citation: ama: Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287 apa: Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287 chicago: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287. ieee: Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022. ista: Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216. mla: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287. short: Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216. corr_author: '1' date_created: 2020-03-09T07:06:52Z date_published: 2022-01-01T00:00:00Z date_updated: 2024-11-04T13:52:44Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1080/00036811.2020.1736287 ec_funded: 1 external_id: arxiv: - '2101.08057' isi: - '000518364100001' file: - access_level: open_access checksum: 869efe8cb09505dfa6012f67d20db63d content_type: application/pdf creator: dernst date_created: 2020-10-12T10:42:54Z date_updated: 2021-03-16T23:30:06Z embargo: 2021-03-15 file_id: '8648' file_name: 2020_ApplicAnalysis_Shehu.pdf file_size: 4282586 relation: main_file file_date_updated: 2021-03-16T23:30:06Z has_accepted_license: '1' intvolume: ' 101' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 192-216 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applicable Analysis publication_identifier: eissn: - 1563-504X issn: - 0003-6811 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Weak convergence for variational inequalities with inertial-type method type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 101 year: '2022' ... --- _id: '10552' abstract: - lang: eng text: We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y) where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h∗ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for fP and an efficient proximal map for h∗ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n2) convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0} then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision. acknowledgement: Vladimir Kolmogorov was supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160. Thomas Pock acknowledges support by an ERC grant HOMOVIS, no 640156. article_processing_charge: No arxiv: 1 author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Thomas full_name: Pock, Thomas last_name: Pock citation: ama: 'Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.' apa: Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual. chicago: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021. ieee: V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021. ista: 'Kolmogorov V, Pock T. 2021. One-sided Frank-Wolfe algorithms for saddle problems. 38th International Conference on Machine Learning. ICML: International Conference on Machine Learning.' mla: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” 38th International Conference on Machine Learning, 2021. short: V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning, 2021. conference: end_date: 2021-07-24 location: Virtual name: 'ICML: International Conference on Machine Learning' start_date: 2021-07-18 corr_author: '1' date_created: 2021-12-16T12:41:20Z date_published: 2021-07-01T00:00:00Z date_updated: 2025-07-16T08:04:23Z day: '01' department: - _id: VlKo ec_funded: 1 external_id: arxiv: - '2101.12617' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.12617 month: '07' oa: 1 oa_version: Preprint project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: 38th International Conference on Machine Learning publication_status: published quality_controlled: '1' scopus_import: '1' status: public title: One-sided Frank-Wolfe algorithms for saddle problems type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2021' ...