--- _id: '14364' abstract: - lang: eng text: We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve -set agreement among processes or approximate agreement on a cycle of length 4 among processes in a wait-free manner in asynchronous models where processes communicate using objects that can be constructed from shared registers. However, it was unknown whether proofs based on simpler techniques were possible. We show that these impossibility results cannot be obtained by extension-based proofs in the iterated snapshot model and, hence, extension-based proofs are limited in power. acknowledgement: "We would like to thank Valerie King, Toniann Pitassi, and Michael Saks for helpful discussions and Shi Hao Liu for his useful feedback.\r\nThis research was supported by the Natural Science and Engineering Research Council of Canada under grants RGPIN-2015-05080 and RGPIN-2020-04178, a postgraduate scholarship, and a postdoctoral fellowship; a University of Toronto postdoctoral fellowship; the National Science Foundation under grants CCF-1217921, CCF-1301926, CCF-1637385, CCF-1650596, and IIS-1447786; the U.S. Department of Energy under grant ER26116/DE-SC0008923; the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement 805223 ScaleML; and the Oracle and Intel corporations. Some of the work on this paper was done while Faith Ellen was visiting IST Austria." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X - first_name: James full_name: Aspnes, James last_name: Aspnes - first_name: Faith full_name: Ellen, Faith last_name: Ellen - first_name: Rati full_name: Gelashvili, Rati last_name: Gelashvili - first_name: Leqi full_name: Zhu, Leqi id: a2117c59-cee4-11ed-b9d0-874ecf0f8ac5 last_name: Zhu citation: ama: Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. Why extension-based proofs fail. SIAM Journal on Computing. 2023;52(4):913-944. doi:10.1137/20M1375851 apa: Alistarh, D.-A., Aspnes, J., Ellen, F., Gelashvili, R., & Zhu, L. (2023). Why extension-based proofs fail. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1375851 chicago: Alistarh, Dan-Adrian, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. “Why Extension-Based Proofs Fail.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/20M1375851. ieee: D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, and L. Zhu, “Why extension-based proofs fail,” SIAM Journal on Computing, vol. 52, no. 4. Society for Industrial and Applied Mathematics, pp. 913–944, 2023. ista: Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. 2023. Why extension-based proofs fail. SIAM Journal on Computing. 52(4), 913–944. mla: Alistarh, Dan-Adrian, et al. “Why Extension-Based Proofs Fail.” SIAM Journal on Computing, vol. 52, no. 4, Society for Industrial and Applied Mathematics, 2023, pp. 913–44, doi:10.1137/20M1375851. short: D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, L. Zhu, SIAM Journal on Computing 52 (2023) 913–944. date_created: 2023-09-24T22:01:11Z date_published: 2023-07-25T00:00:00Z date_updated: 2025-05-14T11:26:06Z day: '25' department: - _id: DaAl doi: 10.1137/20M1375851 ec_funded: 1 external_id: arxiv: - '1811.01421' isi: - '001082972300004' intvolume: ' 52' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1811.01421 month: '07' oa: 1 oa_version: Preprint page: 913-944 project: - _id: 268A44D6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '805223' name: Elastic Coordination for Scalable Machine Learning publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '6676' relation: earlier_version status: public scopus_import: '1' status: public title: Why extension-based proofs fail type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 52 year: '2023' ... --- _id: '14558' abstract: - lang: eng text: "n the dynamic minimum set cover problem, the challenge is to minimize the update time while guaranteeing a close-to-optimal min{O(log n), f} approximation factor. (Throughout, n, m, f , and C are parameters denoting the maximum number of elements, the number of sets, the frequency, and the cost range.) In the high-frequency range, when f = Ω(log n) , this was achieved by a deterministic O(log n) -approximation algorithm with O(f log n) amortized update time by Gupta et al. [Online and dynamic algorithms for set cover, in Proceedings STOC 2017, ACM, pp. 537–550]. In this paper we consider the low-frequency range, when f = O(log n) , and obtain deterministic algorithms with a (1 + ∈)f -approximation ratio and the following guarantees on the update time. (1) O ((f/∈)-log(Cn)) amortized update time: Prior to our work, the best approximation ratio guaranteed by deterministic algorithms was O(f2) of Bhattacharya, Henzinger, and Italiano [Design of dynamic algorithms via primal-dual method, in Proceedings ICALP 2015, Springer, pp. 206–218]. In contrast, the only result with O(f) -approximation was that of Abboud et al. [Dynamic set cover: Improved algorithms and lower bounds, in Proceedings STOC 2019, ACM, pp. 114–125], who designed a randomized (1+∈)f -approximation algorithm with amortized update time. (2) O(f2/∈3 + (f/∈2).logC) amortized update time: This result improves the above update time bound for most values of f\r\n in the low-frequency range, i.e., f=o(log n) . It is also the first result that is independent of m\r\n and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [Deterministically maintaining a (2 + ∈) -approximate minimum vertex cover in O(1/∈2) amortized update time, in Proceedings SODA 2019, SIAM, pp. 1872–1885] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). (3) O((f/∈3).log2(Cn)) worst-case update time: No nontrivial worst-case update time was previously known for the dynamic set cover problem. Our bound subsumes and improves by a logarithmic factor the O(log3n/poly (∈)) \r\n worst-case update time for the unweighted dynamic vertex cover problem (i.e., when f = 2\r\n and C =1) of Bhattacharya, Henzinger, and Nanongkai [Fully dynamic approximate maximum matching and minimum vertex cover in O(log3)n worst case update time, in Proceedings SODA 2017, SIAM, pp. 470–489]. We achieve our results via the primal-dual approach, by maintaining a fractional packing solution as a dual certificate. Prior work in dynamic algorithms that employs the primal-dual approach uses a local update scheme that maintains relaxed complementary slackness conditions for every set. For our first result we use instead a global update scheme that does not always maintain complementary slackness conditions. For our second result we combine the global and the local update schema. To achieve our third result we use a hierarchy of background schedulers. It is an interesting open question whether this background scheduler technique can also be used to transform algorithms with amortized running time bounds into algorithms with worst-case running time bounds." acknowledgement: "This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grants 715672 and\r\n101019564 ``The Design of Modern Fully Dynamic Data Structures (MoDynStruct)\"\") and from the Engineering and Physical Sciences Research Council, UK (EPSRC) under grant EP/S03353X/1. The second author was also supported by the Austrian Science Fund (FWF) project ``Fast Algorithms for a Reactive Network Layer (ReactNet),\"\" P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020--2024, project ``Static and Dynamic Hierarchical Graph Decompositions,\"\"I 5982-N, and project Z 422-N. The third author was also supported by the Swedish Research Council (Reg. No. 2015-04659). The fourth author was also supported by the Science and Technology Development Fund (FDCT), Macau SAR (file 0014/2022/AFJ, 0085/2022/A, 0143/2020/A3, and SKL-IOTSC-2021-2023)." article_processing_charge: No article_type: original author: - first_name: Sayan full_name: Bhattacharya, Sayan last_name: Bhattacharya - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Danupon full_name: Nanongkai, Danupon last_name: Nanongkai - first_name: Xiaowei full_name: Wu, Xiaowei last_name: Wu citation: ama: Bhattacharya S, Henzinger M, Nanongkai D, Wu X. Deterministic near-optimal approximation algorithms for dynamic set cover. SIAM Journal on Computing. 2023;52(5):1132-1192. doi:10.1137/21M1428649 apa: Bhattacharya, S., Henzinger, M., Nanongkai, D., & Wu, X. (2023). Deterministic near-optimal approximation algorithms for dynamic set cover. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1428649 chicago: Bhattacharya, Sayan, Monika Henzinger, Danupon Nanongkai, and Xiaowei Wu. “Deterministic Near-Optimal Approximation Algorithms for Dynamic Set Cover.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1428649. ieee: S. Bhattacharya, M. Henzinger, D. Nanongkai, and X. Wu, “Deterministic near-optimal approximation algorithms for dynamic set cover,” SIAM Journal on Computing, vol. 52, no. 5. Society for Industrial and Applied Mathematics, pp. 1132–1192, 2023. ista: Bhattacharya S, Henzinger M, Nanongkai D, Wu X. 2023. Deterministic near-optimal approximation algorithms for dynamic set cover. SIAM Journal on Computing. 52(5), 1132–1192. mla: Bhattacharya, Sayan, et al. “Deterministic Near-Optimal Approximation Algorithms for Dynamic Set Cover.” SIAM Journal on Computing, vol. 52, no. 5, Society for Industrial and Applied Mathematics, 2023, pp. 1132–92, doi:10.1137/21M1428649. short: S. Bhattacharya, M. Henzinger, D. Nanongkai, X. Wu, SIAM Journal on Computing 52 (2023) 1132–1192. date_created: 2023-11-19T23:00:56Z date_published: 2023-10-01T00:00:00Z date_updated: 2025-09-09T13:19:49Z day: '01' department: - _id: MoHe doi: 10.1137/21M1428649 ec_funded: 1 external_id: isi: - '001116719500002' intvolume: ' 52' isi: 1 issue: '5' language: - iso: eng month: '10' oa_version: None page: 1132-1192 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Deterministic near-optimal approximation algorithms for dynamic set cover type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 52 year: '2023' ... --- _id: '12563' abstract: - lang: eng text: 'he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems.' acknowledgement: "Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\x1Eects only the authors’ views and not the views of the ERC or the European Commission. " article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Andrei full_name: Krokhin, Andrei last_name: Krokhin - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 - first_name: Marcin full_name: Wrochna, Marcin last_name: Wrochna - first_name: Stanislav full_name: Živný, Stanislav last_name: Živný citation: ama: Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 2023;52(1):38-79. doi:10.1137/20m1378223 apa: Krokhin, A., Opršal, J., Wrochna, M., & Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20m1378223 chicago: Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/20m1378223. ieee: A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” SIAM Journal on Computing, vol. 52, no. 1. Society for Industrial and Applied Mathematics, pp. 38–79, 2023. ista: Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79. mla: Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing, vol. 52, no. 1, Society for Industrial and Applied Mathematics, 2023, pp. 38–79, doi:10.1137/20m1378223. short: A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79. date_created: 2023-02-16T07:03:52Z date_published: 2023-01-01T00:00:00Z date_updated: 2025-05-14T10:51:32Z day: '01' department: - _id: UlWa doi: 10.1137/20m1378223 ec_funded: 1 external_id: arxiv: - '2003.11351' isi: - '000955000000001' intvolume: ' 52' isi: 1 issue: '1' keyword: - General Mathematics - General Computer Science language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2003.11351 month: '01' oa: 1 oa_version: Preprint page: 38-79 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Topology and adjunction in promise constraint satisfaction type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 52 year: '2023' ... --- _id: '12960' abstract: - lang: eng text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M^ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. " acknowledgement: The authors have received funding from the European Research Council under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations of Geometric Un-derstanding in Higher Dimensions). The first author was supported by the French government,through the 3IA C\^ote d'Azur Investments in the Future project managed by the National ResearchAgency (ANR) with the reference ANR-19-P3IA-0002. The third author was supported by the Eu-ropean Union's Horizon 2020 research and innovation programme under the Marie Sk\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science Fund) grant M 3073. article_processing_charge: No article_type: original author: - first_name: Jean Daniel full_name: Boissonnat, Jean Daniel last_name: Boissonnat - first_name: Siargey full_name: Kachanovich, Siargey last_name: Kachanovich - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918 apa: Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918 chicago: Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918. ieee: J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023. ista: Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 52(2), 452–486. mla: Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:10.1137/21M1412918. short: J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486. corr_author: '1' date_created: 2023-05-14T22:01:00Z date_published: 2023-04-30T00:00:00Z date_updated: 2025-04-15T06:54:46Z day: '30' department: - _id: HeEd doi: 10.1137/21M1412918 ec_funded: 1 external_id: isi: - '001013183000012' intvolume: ' 52' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1 month: '04' oa: 1 oa_version: Submitted Version page: 452-486 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '9441' relation: earlier_version status: public scopus_import: '1' status: public title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 52 year: '2023' ... --- _id: '11886' abstract: - lang: eng text: "We present a deterministic (1+\U0001D45C(1))-approximation (\U0001D45B1/2+\U0001D45C(1)+\U0001D4371+\U0001D45C(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \\sf CONGEST model); here \U0001D45B is the number of nodes in the network, \U0001D437 is its (hop) diameter, and edge weights are positive integers from 1 to poly(\U0001D45B). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+\U0001D45C(1))-approximation \U0001D442̃ (\U0001D45B√\U0001D4371/4+\U0001D437)-time algorithm of Nanongkai [in Proceedings of STOC, 2014, pp. 565--573] by a factor of as large as \U0001D45B1/8, and (ii) the \U0001D442(\U0001D716−1log\U0001D716−1)-approximation factor of Lenzen and Patt-Shamir's \U0001D442̃ (\U0001D45B1/2+\U0001D716+\U0001D437)-time algorithm [in Proceedings of STOC, 2013, pp. 381--390] within the same running time. (Throughout, we use \U0001D442̃ (⋅) to hide polylogarithmic factors in \U0001D45B.) Our running time matches the known time lower bound of Ω(\U0001D45B/log\U0001D45B‾‾‾‾‾‾‾√+\U0001D437) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40--57]. It also implies a (2+\U0001D45C(1))-approximation (\U0001D45B1/2+\U0001D45C(1)+\U0001D4371+\U0001D45C(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (\U0001D45B\U0001D45C(1),\U0001D45C(1))-hop set of size \U0001D45B1+\U0001D45C(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434--446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375--382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153--162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+\U0001D45C(1))-approximation \U0001D45B\U0001D45C(1)-time algorithm on congested cliques, and (ii) a (1+\U0001D45C(1))-approximation \U0001D45B\U0001D45C(1)-pass \U0001D45B1+\U0001D45C(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565--573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14]." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Sebastian full_name: Krinninger, Sebastian last_name: Krinninger - first_name: Danupon full_name: Nanongkai, Danupon last_name: Nanongkai citation: ama: Henzinger M, Krinninger S, Nanongkai D. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. SIAM Journal on Computing. 2021;50(3):STOC16-98-STOC16-137. doi:10.1137/16m1097808 apa: Henzinger, M., Krinninger, S., & Nanongkai, D. (2021). A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/16m1097808 chicago: Henzinger, Monika, Sebastian Krinninger, and Danupon Nanongkai. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2021. https://doi.org/10.1137/16m1097808. ieee: M. Henzinger, S. Krinninger, and D. Nanongkai, “A deterministic almost-tight distributed algorithm for approximating single-source shortest paths,” SIAM Journal on Computing, vol. 50, no. 3. Society for Industrial & Applied Mathematics, pp. STOC16-98-STOC16-137, 2021. ista: Henzinger M, Krinninger S, Nanongkai D. 2021. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. SIAM Journal on Computing. 50(3), STOC16-98-STOC16-137. mla: Henzinger, Monika, et al. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” SIAM Journal on Computing, vol. 50, no. 3, Society for Industrial & Applied Mathematics, 2021, pp. STOC16-98-STOC16-137, doi:10.1137/16m1097808. short: M. Henzinger, S. Krinninger, D. Nanongkai, SIAM Journal on Computing 50 (2021) STOC16-98-STOC16-137. date_created: 2022-08-17T07:54:45Z date_published: 2021-05-01T00:00:00Z date_updated: 2024-11-06T12:22:31Z day: '01' doi: 10.1137/16m1097808 extern: '1' external_id: arxiv: - '1504.07056' intvolume: ' 50' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1504.07056 month: '05' oa: 1 oa_version: Preprint page: STOC16-98-STOC16-137 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: A deterministic almost-tight distributed algorithm for approximating single-source shortest paths type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2021' ... --- _id: '15271' abstract: - lang: eng text: 'We settle the complexity of the (∆ + 1)-coloring and (∆ + 1)-list coloring problems intheCONGESTED CLIQUEmodel by presenting a simpledeterministicalgorithm for both problemsrunning in a constant number of rounds. This matches the complexity of the recent breakthroughrandomizedconstant-round (∆ + 1)-list coloring algorithm due to Chang et al. [Proceedings of the38th ACM Symposium on Principles of Distributed Computing, 2019] and significantly improvesupon the state-of-the-artO(log ∆)-round deterministic (∆ + 1)-coloring bound of Parter [Proceed-ings of the 45th Annual International Colloquium on Automata, Languages and Programming]. Aremarkable property of our algorithm is its simplicity. Whereas the state-of-the-artrandomizedal-gorithms for this problem are based on the quite involved local coloring algorithm of Chang, Li, andPettie [Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018],our algorithm can be described in just a few lines. At a high level, it applies a careful derandomiza-tion of a recursive procedure which partitions the nodes and their respective palettes into separatebins. We show that afterO(1) recursion steps, the remaining uncolored subgraph within each bin haslinear size and thus can be solved locally by collecting it to a single node. This algorithm can alsobe implemented in the massively parallel computation (MPC) model provided that each machine haslinear (inn, the number of nodes in the input graph) space. We also show an extension of our algo-rithm to theMPCregime, in which machines havesublinearspace: we present the first deterministic(∆ + 1)-list coloring algorithm designed for sublinear-spaceMPC, which runs inO(log ∆ + log logn)rounds.' acknowledgement: The first author was partially supported by the Centre for Discrete Mathematics and its Applications, by the IBM Faculty Award, and by the EPSRC award EP/N011163/1. The second author was partially supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement 754411. The first and third authors were partially supported by a Weizmann-UK Making Connections grant. article_processing_charge: No article_type: original author: - first_name: Artur full_name: Czumaj, Artur last_name: Czumaj - first_name: Peter full_name: Davies, Peter id: 11396234-BB50-11E9-B24C-90FCE5697425 last_name: Davies orcid: 0000-0002-5646-9524 - first_name: Merav full_name: Parter, Merav last_name: Parter citation: ama: Czumaj A, Davies P, Parter M. Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. 2021;50(5):1603-1626. doi:10.1137/20m1366502 apa: Czumaj, A., Davies, P., & Parter, M. (2021). Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20m1366502 chicago: Czumaj, Artur, Peter Davies, and Merav Parter. “Simple, Deterministic, Constant-Round Coloring in Congested Clique and MPC.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/20m1366502. ieee: A. Czumaj, P. Davies, and M. Parter, “Simple, deterministic, constant-round coloring in congested clique and MPC,” SIAM Journal on Computing, vol. 50, no. 5. Society for Industrial and Applied Mathematics, pp. 1603–1626, 2021. ista: Czumaj A, Davies P, Parter M. 2021. Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. 50(5), 1603–1626. mla: Czumaj, Artur, et al. “Simple, Deterministic, Constant-Round Coloring in Congested Clique and MPC.” SIAM Journal on Computing, vol. 50, no. 5, Society for Industrial and Applied Mathematics, 2021, pp. 1603–26, doi:10.1137/20m1366502. short: A. Czumaj, P. Davies, M. Parter, SIAM Journal on Computing 50 (2021) 1603–1626. date_created: 2024-04-03T07:53:22Z date_published: 2021-01-01T00:00:00Z date_updated: 2025-09-10T10:14:11Z day: '01' department: - _id: DaAl doi: 10.1137/20m1366502 ec_funded: 1 external_id: isi: - '000713008600004' intvolume: ' 50' isi: 1 issue: '5' keyword: - General Mathematics - General Computer Science language: - iso: eng month: '01' oa_version: None page: 1603-1626 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Simple, deterministic, constant-round coloring in congested clique and MPC type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 50 year: '2021' ... --- _id: '11889' abstract: - lang: eng text: "We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic \U0001D442(\U0001D45Alog2\U0001D45Bloglog2\U0001D45B) time algorithm. This improves on both the best previously known deterministic running time of \U0001D442(\U0001D45Alog12\U0001D45B) (Kawarabayashi and Thorup [J. ACM, 66 (2018), 4]) and the best previously known randomized running time of \U0001D442(\U0001D45Alog3\U0001D45B) (Karger [J. ACM, 47 (2000), pp. 46--76]) for this problem, though Karger's algorithm can be further applied to weighted graphs. Moreover, our result extends to balanced directed graphs, where the balance of a directed graph captures how close the graph is to being Eulerian. Our approach is using the Kawarabayashi and Thorup graph compression technique, which repeatedly finds low conductance cuts. To find these cuts they use a diffusion-based local algorithm. We use instead a flow-based local algorithm and suitably adjust their framework to work with our flow-based subroutine. Both flow- and diffusion-based methods have a long history of being applied to finding low conductance cuts. Diffusion algorithms have several variants that are naturally local, while it is more complicated to make flow methods local. Some prior work has proven nice properties for local flow-based algorithms with respect to improving or cleaning up low conductance cuts. Our flow subroutine, however, is the first that both is local and produces low conductance cuts. Thus, it may be of independent interest." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Satish full_name: Rao, Satish last_name: Rao - first_name: Di full_name: Wang, Di last_name: Wang citation: ama: Henzinger M, Rao S, Wang D. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 2020;49(1):1-36. doi:10.1137/18m1180335 apa: Henzinger, M., Rao, S., & Wang, D. (2020). Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/18m1180335 chicago: Henzinger, Monika, Satish Rao, and Di Wang. “Local Flow Partitioning for Faster Edge Connectivity.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2020. https://doi.org/10.1137/18m1180335. ieee: M. Henzinger, S. Rao, and D. Wang, “Local flow partitioning for faster edge connectivity,” SIAM Journal on Computing, vol. 49, no. 1. Society for Industrial & Applied Mathematics, pp. 1–36, 2020. ista: Henzinger M, Rao S, Wang D. 2020. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 49(1), 1–36. mla: Henzinger, Monika, et al. “Local Flow Partitioning for Faster Edge Connectivity.” SIAM Journal on Computing, vol. 49, no. 1, Society for Industrial & Applied Mathematics, 2020, pp. 1–36, doi:10.1137/18m1180335. short: M. Henzinger, S. Rao, D. Wang, SIAM Journal on Computing 49 (2020) 1–36. date_created: 2022-08-17T08:09:31Z date_published: 2020-01-01T00:00:00Z date_updated: 2024-11-06T12:22:42Z day: '01' doi: 10.1137/18m1180335 extern: '1' external_id: arxiv: - '1704.01254' intvolume: ' 49' issue: '1' language: - iso: eng main_file_link: - url: https://arxiv.org/abs/1704.01254 month: '01' oa_version: Preprint page: 1-36 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' related_material: record: - id: '11873' relation: later_version status: public scopus_import: '1' status: public title: Local flow partitioning for faster edge connectivity type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2020' ... --- _id: '6672' abstract: - lang: eng text: The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This structure has been implemented and was shown to lead to good triangulations in $\mathbb{R}^2$ and on surfaces embedded in $\mathbb{R}^3$ as detailed in our experimental companion paper. In this paper, we study theoretical aspects of our structure. Given a finite set of points $\mathcal{P}$ in a domain $\Omega$ equipped with a Riemannian metric, we compare the discrete Riemannian Voronoi diagram of $\mathcal{P}$ to its Riemannian Voronoi diagram. Both diagrams have dual structures called the discrete Riemannian Delaunay and the Riemannian Delaunay complex. We provide conditions that guarantee that these dual structures are identical. It then follows from previous results that the discrete Riemannian Delaunay complex can be embedded in $\Omega$ under sufficient conditions, leading to an anisotropic triangulation with curved simplices. Furthermore, we show that, under similar conditions, the simplices of this triangulation can be straightened. arxiv: 1 author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: Mael full_name: Rouxel-Labbé, Mael last_name: Rouxel-Labbé - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat J-D, Rouxel-Labbé M, Wintraecken M. Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. 2019;48(3):1046-1097. doi:10.1137/17m1152292 apa: Boissonnat, J.-D., Rouxel-Labbé, M., & Wintraecken, M. (2019). Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. Society for Industrial & Applied Mathematics (SIAM). https://doi.org/10.1137/17m1152292 chicago: Boissonnat, Jean-Daniel, Mael Rouxel-Labbé, and Mathijs Wintraecken. “Anisotropic Triangulations via Discrete Riemannian Voronoi Diagrams.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics (SIAM), 2019. https://doi.org/10.1137/17m1152292. ieee: J.-D. Boissonnat, M. Rouxel-Labbé, and M. Wintraecken, “Anisotropic triangulations via discrete Riemannian Voronoi diagrams,” SIAM Journal on Computing, vol. 48, no. 3. Society for Industrial & Applied Mathematics (SIAM), pp. 1046–1097, 2019. ista: Boissonnat J-D, Rouxel-Labbé M, Wintraecken M. 2019. Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. 48(3), 1046–1097. mla: Boissonnat, Jean-Daniel, et al. “Anisotropic Triangulations via Discrete Riemannian Voronoi Diagrams.” SIAM Journal on Computing, vol. 48, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2019, pp. 1046–97, doi:10.1137/17m1152292. short: J.-D. Boissonnat, M. Rouxel-Labbé, M. Wintraecken, SIAM Journal on Computing 48 (2019) 1046–1097. date_created: 2019-07-24T08:42:12Z date_published: 2019-05-21T00:00:00Z date_updated: 2021-01-12T08:08:30Z day: '21' doi: 10.1137/17m1152292 extern: '1' external_id: arxiv: - '1703.06487' intvolume: ' 48' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1703.06487 month: '05' oa: 1 oa_version: Preprint page: 1046-1097 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) quality_controlled: '1' status: public title: Anisotropic triangulations via discrete Riemannian Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2019' ... --- _id: '7412' abstract: - lang: eng text: We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These algorithms search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a random nearby state that addresses the violation, while (we hope) not introducing many new violations. An important class of focused local search algorithms with provable performance guarantees has recently arisen from algorithmizations of the Lovász local lemma (LLL), a nonconstructive tool for proving the existence of satisfying states by introducing a background measure on the state space. While powerful, the state transitions of algorithms in this class must be, in a precise sense, perfectly compatible with the background measure. In many applications this is a very restrictive requirement, and one needs to step outside the class. Here we introduce the notion of measure distortion and develop a framework for analyzing arbitrary focused stochastic local search algorithms, recovering LLL algorithmizations as the special case of no distortion. Our framework takes as input an arbitrary algorithm of such type and an arbitrary probability measure and shows how to use the measure as a yardstick of algorithmic progress, even for algorithms designed independently of the measure. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Dimitris full_name: Achlioptas, Dimitris last_name: Achlioptas - first_name: Fotis full_name: Iliopoulos, Fotis last_name: Iliopoulos - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Achlioptas D, Iliopoulos F, Kolmogorov V. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 2019;48(5):1583-1602. doi:10.1137/16m109332x apa: Achlioptas, D., Iliopoulos, F., & Kolmogorov, V. (2019). A local lemma for focused stochastical algorithms. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16m109332x chicago: Achlioptas, Dimitris, Fotis Iliopoulos, and Vladimir Kolmogorov. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing. SIAM, 2019. https://doi.org/10.1137/16m109332x. ieee: D. Achlioptas, F. Iliopoulos, and V. Kolmogorov, “A local lemma for focused stochastical algorithms,” SIAM Journal on Computing, vol. 48, no. 5. SIAM, pp. 1583–1602, 2019. ista: Achlioptas D, Iliopoulos F, Kolmogorov V. 2019. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 48(5), 1583–1602. mla: Achlioptas, Dimitris, et al. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing, vol. 48, no. 5, SIAM, 2019, pp. 1583–602, doi:10.1137/16m109332x. short: D. Achlioptas, F. Iliopoulos, V. Kolmogorov, SIAM Journal on Computing 48 (2019) 1583–1602. date_created: 2020-01-30T09:27:32Z date_published: 2019-10-31T00:00:00Z date_updated: 2024-11-04T13:52:36Z day: '31' department: - _id: VlKo doi: 10.1137/16m109332x ec_funded: 1 external_id: arxiv: - '1809.01537' isi: - '000493900200005' intvolume: ' 48' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1809.01537 month: '10' oa: 1 oa_version: Preprint page: 1583-1602 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: '1' status: public title: A local lemma for focused stochastical algorithms type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 48 year: '2019' ... --- _id: '11890' abstract: - lang: eng text: "We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph \U0001D43A=(\U0001D449,\U0001D438), with |\U0001D449|=\U0001D45B and |\U0001D438|=\U0001D45A, in \U0001D45C(\U0001D45A‾‾√) time per update. In particular, for minimum vertex cover, we provide deterministic data structures for maintaining a (2+\U0001D716) approximation in \U0001D442(log\U0001D45B/\U0001D7162) amortized time per update. For maximum matching, we show how to maintain a (3+\U0001D716) approximation in \U0001D442(min(\U0001D45B√/\U0001D716,\U0001D45A1/3/\U0001D7162) amortized time per update and a (4+\U0001D716) approximation in \U0001D442(\U0001D45A1/3/\U0001D7162) worst-case time per update. Our data structure for fully dynamic minimum vertex cover is essentially near-optimal and settles an open problem by Onak and Rubinfeld [in 42nd ACM Symposium on Theory of Computing, Cambridge, MA, ACM, 2010, pp. 457--464]." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Sayan full_name: Bhattacharya, Sayan last_name: Bhattacharya - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Giuseppe F. full_name: Italiano, Giuseppe F. last_name: Italiano citation: ama: Bhattacharya S, Henzinger M, Italiano GF. Deterministic fully dynamic data structures for vertex cover and matching. SIAM Journal on Computing. 2018;47(3):859-887. doi:10.1137/140998925 apa: Bhattacharya, S., Henzinger, M., & Italiano, G. F. (2018). Deterministic fully dynamic data structures for vertex cover and matching. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/140998925 chicago: Bhattacharya, Sayan, Monika Henzinger, and Giuseppe F. Italiano. “Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2018. https://doi.org/10.1137/140998925. ieee: S. Bhattacharya, M. Henzinger, and G. F. Italiano, “Deterministic fully dynamic data structures for vertex cover and matching,” SIAM Journal on Computing, vol. 47, no. 3. Society for Industrial & Applied Mathematics, pp. 859–887, 2018. ista: Bhattacharya S, Henzinger M, Italiano GF. 2018. Deterministic fully dynamic data structures for vertex cover and matching. SIAM Journal on Computing. 47(3), 859–887. mla: Bhattacharya, Sayan, et al. “Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching.” SIAM Journal on Computing, vol. 47, no. 3, Society for Industrial & Applied Mathematics, 2018, pp. 859–87, doi:10.1137/140998925. short: S. Bhattacharya, M. Henzinger, G.F. Italiano, SIAM Journal on Computing 47 (2018) 859–887. date_created: 2022-08-17T08:21:23Z date_published: 2018-05-01T00:00:00Z date_updated: 2024-11-06T12:22:54Z day: '01' doi: 10.1137/140998925 extern: '1' external_id: arxiv: - '1412.1318' intvolume: ' 47' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1412.1318 month: '05' oa: 1 oa_version: Preprint page: 859-887 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' related_material: record: - id: '11875' relation: earlier_version status: public scopus_import: '1' status: public title: Deterministic fully dynamic data structures for vertex cover and matching type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2018' ... --- _id: '5975' abstract: - lang: eng text: We consider the recent formulation of the algorithmic Lov ́asz Local Lemma [N. Har-vey and J. Vondr ́ak, inProceedings of FOCS, 2015, pp. 1327–1345; D. Achlioptas and F. Iliopoulos,inProceedings of SODA, 2016, pp. 2024–2038; D. Achlioptas, F. Iliopoulos, and V. Kolmogorov,ALocal Lemma for Focused Stochastic Algorithms, arXiv preprint, 2018] for finding objects that avoid“bad features,” or “flaws.” It extends the Moser–Tardos resampling algorithm [R. A. Moser andG. Tardos,J. ACM, 57 (2010), 11] to more general discrete spaces. At each step the method picks aflaw present in the current state and goes to a new state according to some prespecified probabilitydistribution (which depends on the current state and the selected flaw). However, the recent formu-lation is less flexible than the Moser–Tardos method since it requires a specific flaw selection rule,whereas the algorithm of Moser and Tardos allows an arbitrary rule (and thus can potentially beimplemented more efficiently). We formulate a new “commutativity” condition and prove that it issufficient for an arbitrary rule to work. It also enables an efficient parallelization under an additionalassumption. We then show that existing resampling oracles for perfect matchings and permutationsdo satisfy this condition. 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. Commutativity in the algorithmic Lovász local lemma. SIAM Journal on Computing. 2018;47(6):2029-2056. doi:10.1137/16m1093306 apa: Kolmogorov, V. (2018). Commutativity in the algorithmic Lovász local lemma. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/16m1093306 chicago: Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2018. https://doi.org/10.1137/16m1093306. ieee: V. Kolmogorov, “Commutativity in the algorithmic Lovász local lemma,” SIAM Journal on Computing, vol. 47, no. 6. Society for Industrial and Applied Mathematics, pp. 2029–2056, 2018. ista: Kolmogorov V. 2018. Commutativity in the algorithmic Lovász local lemma. SIAM Journal on Computing. 47(6), 2029–2056. mla: Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” SIAM Journal on Computing, vol. 47, no. 6, Society for Industrial and Applied Mathematics, 2018, pp. 2029–56, doi:10.1137/16m1093306. short: V. Kolmogorov, SIAM Journal on Computing 47 (2018) 2029–2056. date_created: 2019-02-13T12:59:33Z date_published: 2018-11-08T00:00:00Z date_updated: 2025-09-22T09:44:20Z day: '08' department: - _id: VlKo doi: 10.1137/16m1093306 ec_funded: 1 external_id: arxiv: - '1506.08547' isi: - '000453785100001' intvolume: ' 47' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1506.08547 month: '11' oa: 1 oa_version: Preprint page: 2029-2056 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '1193' relation: earlier_version status: public scopus_import: '1' status: public title: Commutativity in the algorithmic Lovász local lemma type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2018' ... --- _id: '11891' abstract: - lang: eng text: "We study dynamic (1+\U0001D716)-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected \U0001D45B-node \U0001D45A-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of \U0001D442̃ (\U0001D45A\U0001D45B/\U0001D716) and constant query time by Roditty and Zwick [SIAM J. Comput., 41 (2012), pp. 670--683]. The fastest deterministic algorithm is from a 1981 paper by Even and Shiloach [J. ACM, 28 (1981), pp. 1--4]; it has a total update time of \U0001D442(\U0001D45A\U0001D45B2) and constant query time. We improve these results as follows: (1) We present an algorithm with a total update time of \U0001D442̃ (\U0001D45B5/2/\U0001D716) and constant query time that has an additive error of 2 in addition to the 1+\U0001D716 multiplicative error. This beats the previous \U0001D442̃ (\U0001D45A\U0001D45B/\U0001D716) time when \U0001D45A=Ω(\U0001D45B3/2). Note that the additive error is unavoidable since, even in the static case, an \U0001D442(\U0001D45B3−\U0001D6FF)-time (a so-called truly subcubic) combinatorial algorithm with 1+\U0001D716 multiplicative error cannot have an additive error less than 2−\U0001D716, unless we make a major breakthrough for Boolean matrix multiplication [D. Dor, S. Halrepin, and U. Zwick, SIAM J. Comput., 29 (2000), pp. 1740--1759] and many other long-standing problems [V. Vassilevska Williams and R. Williams, Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010, pp. 645--654]. The algorithm can also be turned into a (2+\U0001D716)-approximation algorithm (without an additive error) with the same time guarantees, improving the recent (3+\U0001D716)-approximation algorithm with \U0001D442̃ (\U0001D45B5/2+\U0001D442(log(1/\U0001D716)/log\U0001D45B√)) running time of Bernstein and Roditty [Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, 2011, pp. 1355--1365] in terms of both approximation and time guarantees. (2) We present a deterministic algorithm with a total update time of \U0001D442̃ (\U0001D45A\U0001D45B/\U0001D716) and a query time of \U0001D442(loglog\U0001D45B). The algorithm has a multiplicative error of 1+\U0001D716 and gives the first improved deterministic algorithm since 1981. It also answers an open question raised by Bernstein in [Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, 2013, pp. 725--734]. The deterministic algorithm can be turned into a deterministic fully dynamic (1+\U0001D716)-approximation with an amortized update time of \U0001D442̃ (\U0001D45A\U0001D45B/(\U0001D716\U0001D461)) and a query time of \U0001D442̃ (\U0001D461) for every \U0001D461≤\U0001D45B√. In order to achieve our results, we introduce two new techniques: (i) A monotone Even--Shiloach tree algorithm which maintains a bounded-distance shortest-paths tree on a certain type of emulator called a locally persevering emulator. (ii) A derandomization technique based on moving Even--Shiloach trees as a way to derandomize the standard random set argument. These techniques might be of independent interest." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Sebastian full_name: Krinninger, Sebastian last_name: Krinninger - first_name: Danupon full_name: Nanongkai, Danupon last_name: Nanongkai citation: ama: 'Henzinger M, Krinninger S, Nanongkai D. Dynamic approximate all-pairs shortest paths: Breaking the O(mn) barrier and derandomization. SIAM Journal on Computing. 2016;45(3):947-1006. doi:10.1137/140957299' apa: 'Henzinger, M., Krinninger, S., & Nanongkai, D. (2016). Dynamic approximate all-pairs shortest paths: Breaking the O(mn) barrier and derandomization. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/140957299' chicago: 'Henzinger, Monika, Sebastian Krinninger, and Danupon Nanongkai. “Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(Mn) Barrier and Derandomization.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2016. https://doi.org/10.1137/140957299.' ieee: 'M. Henzinger, S. Krinninger, and D. Nanongkai, “Dynamic approximate all-pairs shortest paths: Breaking the O(mn) barrier and derandomization,” SIAM Journal on Computing, vol. 45, no. 3. Society for Industrial & Applied Mathematics, pp. 947–1006, 2016.' ista: 'Henzinger M, Krinninger S, Nanongkai D. 2016. Dynamic approximate all-pairs shortest paths: Breaking the O(mn) barrier and derandomization. SIAM Journal on Computing. 45(3), 947–1006.' mla: 'Henzinger, Monika, et al. “Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(Mn) Barrier and Derandomization.” SIAM Journal on Computing, vol. 45, no. 3, Society for Industrial & Applied Mathematics, 2016, pp. 947–1006, doi:10.1137/140957299.' short: M. Henzinger, S. Krinninger, D. Nanongkai, SIAM Journal on Computing 45 (2016) 947–1006. date_created: 2022-08-17T08:37:00Z date_published: 2016-05-01T00:00:00Z date_updated: 2024-11-06T12:23:06Z day: '01' doi: 10.1137/140957299 extern: '1' external_id: arxiv: - '1308.0776' intvolume: ' 45' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1308.0776 month: '05' oa: 1 oa_version: Preprint page: 947-1006 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: 'Dynamic approximate all-pairs shortest paths: Breaking the O(mn) barrier and derandomization' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2016' ... --- _id: '11892' abstract: - lang: eng text: "We present the first fully dynamic algorithm for maintaining a minimum spanning forest in time \U0001D45C(\U0001D45B√) per operation. To be precise, the algorithm uses O(n1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and bipartiteness in amortized time O(n1/3 log n) per update, with O(1) worst case time per query." article_processing_charge: No article_type: original author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Valerie full_name: King, Valerie last_name: King citation: ama: Henzinger M, King V. Maintaining minimum spanning forests in dynamic graphs. SIAM Journal on Computing. 2001;31(2):364-374. doi:10.1137/s0097539797327209 apa: Henzinger, M., & King, V. (2001). Maintaining minimum spanning forests in dynamic graphs. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/s0097539797327209 chicago: Henzinger, Monika, and Valerie King. “Maintaining Minimum Spanning Forests in Dynamic Graphs.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2001. https://doi.org/10.1137/s0097539797327209. ieee: M. Henzinger and V. King, “Maintaining minimum spanning forests in dynamic graphs,” SIAM Journal on Computing, vol. 31, no. 2. Society for Industrial & Applied Mathematics, pp. 364–374, 2001. ista: Henzinger M, King V. 2001. Maintaining minimum spanning forests in dynamic graphs. SIAM Journal on Computing. 31(2), 364–374. mla: Henzinger, Monika, and Valerie King. “Maintaining Minimum Spanning Forests in Dynamic Graphs.” SIAM Journal on Computing, vol. 31, no. 2, Society for Industrial & Applied Mathematics, 2001, pp. 364–74, doi:10.1137/s0097539797327209. short: M. Henzinger, V. King, SIAM Journal on Computing 31 (2001) 364–374. date_created: 2022-08-17T08:43:43Z date_published: 2001-03-01T00:00:00Z date_updated: 2024-11-06T12:23:16Z day: '01' doi: 10.1137/s0097539797327209 extern: '1' intvolume: ' 31' issue: '2' language: - iso: eng month: '03' oa_version: None page: 364-374 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Maintaining minimum spanning forests in dynamic graphs type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2001' ... --- _id: '11694' abstract: - lang: eng text: We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals. Deng and Papadimitriou [Proceedings of the 31st Symposium on the Foundations of Computer Science, 1990, pp. 356-361] showed an upper bound for R ofd O(d)m and Koutsoupias (reported by Deng and Papadimitriou) gave a lower bound of Ω≠(d2m), where m is the number of edges in the graph and d is the minimum number of edges that have to be added to make the graph Eulerian. We give the 1rst subexponential algorithm for this exploration problem, which achieves an upper bound of dO(logd)m. We also show a matching lower bound of d≠(logd)m for our algorithm. Additionally, we give lower bounds of 2≠(d)m, respectively, d≠(logd)m for various other natural exploration algorithms. acknowledgement: We thank Prabhakar Raghavan for bringing to our attention the literature on the s-t connectivity problem. We also thank an anonymous referee for many helpful comments which improved the presentation of the paper. article_processing_charge: No article_type: original author: - first_name: Susanne full_name: Albers, Susanne last_name: Albers - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 citation: ama: Albers S, Henzinger M. Exploring unknown environments. SIAM Journal on Computing. 2000;29(4):1164-1188. doi:10.1137/s009753979732428x apa: 'Albers, S., & Henzinger, M. (2000). Exploring unknown environments. SIAM Journal on Computing. El Paso, TX, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/s009753979732428x' chicago: Albers, Susanne, and Monika Henzinger. “Exploring Unknown Environments.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2000. https://doi.org/10.1137/s009753979732428x. ieee: S. Albers and M. Henzinger, “Exploring unknown environments,” SIAM Journal on Computing, vol. 29, no. 4. Society for Industrial and Applied Mathematics, pp. 1164–1188, 2000. ista: Albers S, Henzinger M. 2000. Exploring unknown environments. SIAM Journal on Computing. 29(4), 1164–1188. mla: Albers, Susanne, and Monika Henzinger. “Exploring Unknown Environments.” SIAM Journal on Computing, vol. 29, no. 4, Society for Industrial and Applied Mathematics, 2000, pp. 1164–88, doi:10.1137/s009753979732428x. short: S. Albers, M. Henzinger, SIAM Journal on Computing 29 (2000) 1164–1188. conference: end_date: 1997-05-06 location: El Paso, TX, United States name: 'STOC97: 29th Annual Symposium on Theory of Computing' start_date: 1997-05-04 date_created: 2022-07-29T09:04:36Z date_published: 2000-07-01T00:00:00Z date_updated: 2024-11-06T12:09:07Z day: '01' doi: 10.1137/s009753979732428x extern: '1' intvolume: ' 29' issue: '4' keyword: - directed graph - exploration algorithm language: - iso: eng month: '07' oa_version: None page: 1164-1188 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Exploring unknown environments type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 29 year: '2000' ... --- _id: '11893' abstract: - lang: eng text: "We present fully dynamic algorithms for maintaining the biconnected components in general and plane graphs.\r\n\r\nA fully dynamic algorithm maintains a graph during a sequence of insertions and deletions of edges or isolated vertices. Let m be the number of edges and n be the number of vertices in a graph. The time per operation of the best deterministic algorithms is \U0001D442(\U0001D45B√) in general graphs and O(log n) in plane graphs for fully dynamic connectivity and O(min m2/3 ,n}) in general graphs and \U0001D442(\U0001D45B√) in plane graphs for fully dynamic biconnectivity. We improve the later running times to \U0001D442(\U0001D45Alog\U0001D45B‾‾‾‾‾‾‾√) in general graphs and O(log 2n ) in plane graphs. Our algorithm for general graphscan also find the biconnected components of all vertices in time O(n)." article_processing_charge: No article_type: original author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 citation: ama: Henzinger M. Improved data structures for fully dynamic biconnectivity. SIAM Journal on Computing. 2000;29(6):1761-1815. doi:10.1137/s0097539794263907 apa: Henzinger, M. (2000). Improved data structures for fully dynamic biconnectivity. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/s0097539794263907 chicago: Henzinger, Monika. “Improved Data Structures for Fully Dynamic Biconnectivity.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2000. https://doi.org/10.1137/s0097539794263907. ieee: M. Henzinger, “Improved data structures for fully dynamic biconnectivity,” SIAM Journal on Computing, vol. 29, no. 6. Society for Industrial & Applied Mathematics, pp. 1761–1815, 2000. ista: Henzinger M. 2000. Improved data structures for fully dynamic biconnectivity. SIAM Journal on Computing. 29(6), 1761–1815. mla: Henzinger, Monika. “Improved Data Structures for Fully Dynamic Biconnectivity.” SIAM Journal on Computing, vol. 29, no. 6, Society for Industrial & Applied Mathematics, 2000, pp. 1761–815, doi:10.1137/s0097539794263907. short: M. Henzinger, SIAM Journal on Computing 29 (2000) 1761–1815. date_created: 2022-08-17T08:45:41Z date_published: 2000-11-01T00:00:00Z date_updated: 2024-11-06T12:00:56Z day: '01' doi: 10.1137/s0097539794263907 extern: '1' intvolume: ' 29' issue: '6' language: - iso: eng month: '11' oa_version: None page: 1761-1815 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Improved data structures for fully dynamic biconnectivity type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 29 year: '2000' ... --- _id: '4043' abstract: - lang: eng text: It is shown that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). The algorithm is fairly easy to implement and is based on the edge-insertion scheme that iteratively improves an arbitrary initial triangulation. It can be extended to the case where edges are prescribed, and, within the same time- and space-bounds, it can lexicographically minimize the sorted angle vector if the point set is in general position. Experimental results on the efficiency of the algorithm and the quality of the triangulations obtained are included. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Tiow full_name: Tan, Tiow last_name: Tan - first_name: Roman full_name: Waupotitsch, Roman last_name: Waupotitsch citation: ama: Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2 log n) time algorithm for the MinMax angle triangulation. SIAM Journal on Scientific Computing. 1992;13(4):994-1008. doi:10.1137/0913058 apa: Edelsbrunner, H., Tan, T., & Waupotitsch, R. (1992). An O(n^2 log n) time algorithm for the MinMax angle triangulation. SIAM Journal on Scientific Computing. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/0913058 chicago: Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2 Log n) Time Algorithm for the MinMax Angle Triangulation.” SIAM Journal on Scientific Computing. Society for Industrial and Applied Mathematics , 1992. https://doi.org/10.1137/0913058. ieee: H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2 log n) time algorithm for the MinMax angle triangulation,” SIAM Journal on Scientific Computing, vol. 13, no. 4. Society for Industrial and Applied Mathematics , pp. 994–1008, 1992. ista: Edelsbrunner H, Tan T, Waupotitsch R. 1992. An O(n^2 log n) time algorithm for the MinMax angle triangulation. SIAM Journal on Scientific Computing. 13(4), 994–1008. mla: Edelsbrunner, Herbert, et al. “An O(N^2 Log n) Time Algorithm for the MinMax Angle Triangulation.” SIAM Journal on Scientific Computing, vol. 13, no. 4, Society for Industrial and Applied Mathematics , 1992, pp. 994–1008, doi:10.1137/0913058. short: H. Edelsbrunner, T. Tan, R. Waupotitsch, SIAM Journal on Scientific Computing 13 (1992) 994–1008. date_created: 2018-12-11T12:06:36Z date_published: 1992-07-01T00:00:00Z date_updated: 2022-03-16T09:35:05Z day: '01' doi: 10.1137/0913058 extern: '1' intvolume: ' 13' issue: '4' language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/10.1137/0913058 month: '07' oa_version: None page: 994 - 1008 publication: SIAM Journal on Scientific Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '2081' quality_controlled: '1' status: public title: An O(n^2 log n) time algorithm for the MinMax angle triangulation type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 13 year: '1992' ... --- _id: '4051' abstract: - lang: eng text: An algorithm is presented that constructs the convex hull of a set of n points in three dimensions in worst-case time O(n log2h) and storage O(n), where h is the number of extreme points. This is an improvement of the O(nh) time gift-wrapping algorithm and, for certain values of h, of the O(n log n) time divide-and-conquer algorithm. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Weiping full_name: Shi, Weiping last_name: Shi citation: ama: Edelsbrunner H, Shi W. An O(n log^2 h) time algorithm for the three-dimensional convex hull problem. SIAM Journal on Computing. 1991;20(2):259-269. doi:10.1137/0220016 apa: Edelsbrunner, H., & Shi, W. (1991). An O(n log^2 h) time algorithm for the three-dimensional convex hull problem. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0220016 chicago: Edelsbrunner, Herbert, and Weiping Shi. “An O(n Log^2 h) Time Algorithm for the Three-Dimensional Convex Hull Problem.” SIAM Journal on Computing. SIAM, 1991. https://doi.org/10.1137/0220016 . ieee: H. Edelsbrunner and W. Shi, “An O(n log^2 h) time algorithm for the three-dimensional convex hull problem,” SIAM Journal on Computing, vol. 20, no. 2. SIAM, pp. 259–269, 1991. ista: Edelsbrunner H, Shi W. 1991. An O(n log^2 h) time algorithm for the three-dimensional convex hull problem. SIAM Journal on Computing. 20(2), 259–269. mla: Edelsbrunner, Herbert, and Weiping Shi. “An O(n Log^2 h) Time Algorithm for the Three-Dimensional Convex Hull Problem.” SIAM Journal on Computing, vol. 20, no. 2, SIAM, 1991, pp. 259–69, doi:10.1137/0220016 . short: H. Edelsbrunner, W. Shi, SIAM Journal on Computing 20 (1991) 259–269. date_created: 2018-12-11T12:06:39Z date_published: 1991-04-01T00:00:00Z date_updated: 2022-03-02T10:18:31Z day: '01' doi: '10.1137/0220016 ' extern: '1' intvolume: ' 20' issue: '2' language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/10.1137/0220016 month: '04' oa_version: None page: 259 - 269 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM publist_id: '2072' quality_controlled: '1' status: public title: An O(n log^2 h) time algorithm for the three-dimensional convex hull problem type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 20 year: '1991' ... --- _id: '4083' abstract: - lang: eng text: 'It is shown that, given a set S of n points in $R^3 $, one can always find three planes that form an eight-partition of S, that is, a partition where at most ${n / 8}$ points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in $R^3 $. An octant tree for n points occupies $O(n)$ space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in two and three dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circle queries in $R^2 $: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is $T(n) = O(n^\alpha + m)$, where $\alpha = 0.8988$ (or 0.8471 in case (3)), and m is the size of the output. This performance is the best currently known for linear-space data structures that can be deterministically constructed in polynomial time.' article_processing_charge: No article_type: original author: - first_name: F. full_name: Yao, F. last_name: Yao - first_name: David full_name: Dobkin, David last_name: Dobkin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Paterson, Michael last_name: Paterson citation: ama: Yao F, Dobkin D, Edelsbrunner H, Paterson M. Partitioning space for range queries. SIAM Journal on Computing. 1989;18(2):371-384. doi:10.1137/0218025 apa: Yao, F., Dobkin, D., Edelsbrunner, H., & Paterson, M. (1989). Partitioning space for range queries. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0218025 chicago: Yao, F., David Dobkin, Herbert Edelsbrunner, and Michael Paterson. “Partitioning Space for Range Queries.” SIAM Journal on Computing. SIAM, 1989. https://doi.org/10.1137/0218025. ieee: F. Yao, D. Dobkin, H. Edelsbrunner, and M. Paterson, “Partitioning space for range queries,” SIAM Journal on Computing, vol. 18, no. 2. SIAM, pp. 371–384, 1989. ista: Yao F, Dobkin D, Edelsbrunner H, Paterson M. 1989. Partitioning space for range queries. SIAM Journal on Computing. 18(2), 371–384. mla: Yao, F., et al. “Partitioning Space for Range Queries.” SIAM Journal on Computing, vol. 18, no. 2, SIAM, 1989, pp. 371–84, doi:10.1137/0218025. short: F. Yao, D. Dobkin, H. Edelsbrunner, M. Paterson, SIAM Journal on Computing 18 (1989) 371–384. date_created: 2018-12-11T12:06:50Z date_published: 1989-04-01T00:00:00Z date_updated: 2022-02-11T07:55:48Z day: '01' doi: 10.1137/0218025 extern: '1' intvolume: ' 18' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://epubs.siam.org/doi/10.1137/0218025 month: '04' oa: 1 oa_version: Published Version page: 371 - 384 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM publist_id: '2040' quality_controlled: '1' scopus_import: '1' status: public title: Partitioning space for range queries type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 18 year: '1989' ... --- _id: '4091' abstract: - lang: eng text: An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necesssary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known. acknowledgement: The research of this author was supported by the Amoco Foundation Facility for the Development of Computer Science 1-6-44862. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Steven full_name: Skiena, Steven last_name: Skiena citation: ama: Edelsbrunner H, Skiena S. Probing convex polygons with X-Rays. SIAM Journal on Computing. 1988;17(5):870-882. doi:10.1137/0217054 apa: Edelsbrunner, H., & Skiena, S. (1988). Probing convex polygons with X-Rays. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0217054 chicago: Edelsbrunner, Herbert, and Steven Skiena. “Probing Convex Polygons with X-Rays.” SIAM Journal on Computing. SIAM, 1988. https://doi.org/10.1137/0217054 . ieee: H. Edelsbrunner and S. Skiena, “Probing convex polygons with X-Rays,” SIAM Journal on Computing, vol. 17, no. 5. SIAM, pp. 870–882, 1988. ista: Edelsbrunner H, Skiena S. 1988. Probing convex polygons with X-Rays. SIAM Journal on Computing. 17(5), 870–882. mla: Edelsbrunner, Herbert, and Steven Skiena. “Probing Convex Polygons with X-Rays.” SIAM Journal on Computing, vol. 17, no. 5, SIAM, 1988, pp. 870–82, doi:10.1137/0217054 . short: H. Edelsbrunner, S. Skiena, SIAM Journal on Computing 17 (1988) 870–882. date_created: 2018-12-11T12:06:53Z date_published: 1988-01-01T00:00:00Z date_updated: 2022-02-08T11:14:23Z day: '01' doi: '10.1137/0217054 ' extern: '1' intvolume: ' 17' issue: '5' language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/10.1137/0217054 month: '01' oa_version: None page: 870 - 882 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM publist_id: '2030' quality_controlled: '1' scopus_import: '1' status: public title: Probing convex polygons with X-Rays type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 17 year: '1988' ... --- _id: '4104' abstract: - lang: eng text: "Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.\r\n© 1986 Society for Industrial and Applied Mathematics" acknowledgement: We would like to thank Andrei Broder, Dan Greene, Mary Claire van Leunen, Greg Nelson, Lyle Ramshaw, and F. Frances Yao, whose comments and suggestions have greatly improved the readability of this paper. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Leonidas full_name: Guibas, Leonidas last_name: Guibas - first_name: Jorge full_name: Stolfi, Jorge last_name: Stolfi citation: ama: Edelsbrunner H, Guibas L, Stolfi J. Optimal point location in a monotone subdivision. SIAM Journal on Computing. 1986;15(2):317-340. doi:10.1137/0215023 apa: Edelsbrunner, H., Guibas, L., & Stolfi, J. (1986). Optimal point location in a monotone subdivision. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0215023 chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Jorge Stolfi. “Optimal Point Location in a Monotone Subdivision.” SIAM Journal on Computing. SIAM, 1986. https://doi.org/10.1137/0215023. ieee: H. Edelsbrunner, L. Guibas, and J. Stolfi, “Optimal point location in a monotone subdivision,” SIAM Journal on Computing, vol. 15, no. 2. SIAM, pp. 317–340, 1986. ista: Edelsbrunner H, Guibas L, Stolfi J. 1986. Optimal point location in a monotone subdivision. SIAM Journal on Computing. 15(2), 317–340. mla: Edelsbrunner, Herbert, et al. “Optimal Point Location in a Monotone Subdivision.” SIAM Journal on Computing, vol. 15, no. 2, SIAM, 1986, pp. 317–40, doi:10.1137/0215023. short: H. Edelsbrunner, L. Guibas, J. Stolfi, SIAM Journal on Computing 15 (1986) 317–340. date_created: 2018-12-11T12:06:58Z date_published: 1986-01-01T00:00:00Z date_updated: 2022-02-01T10:05:55Z day: '01' doi: 10.1137/0215023 extern: '1' intvolume: ' 15' issue: '2' language: - iso: eng month: '01' oa_version: None page: 317 - 340 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM publist_id: '2016' quality_controlled: '1' scopus_import: '1' status: public title: Optimal point location in a monotone subdivision type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 15 year: '1986' ...