[{"_id":"1612","publication_status":"published","publist_id":"5554","date_published":"2016-02-01T00:00:00Z","month":"02","abstract":[{"lang":"eng","text":"We prove that whenever A is a 3-conservative relational structure with only binary and unary relations,then the algebra of polymorphisms of A either has no Taylor operation (i.e.,CSP(A)is NP-complete),or it generates an SD(∧) variety (i.e.,CSP(A)has bounded width)."}],"department":[{"_id":"VlKo"}],"issue":"1","oa_version":"Preprint","corr_author":"1","arxiv":1,"title":"CSP for binary conservative relational structures","publication":"Algebra Universalis","intvolume":"        75","quality_controlled":"1","isi":1,"citation":{"ama":"Kazda A. CSP for binary conservative relational structures. <i>Algebra Universalis</i>. 2016;75(1):75-84. doi:<a href=\"https://doi.org/10.1007/s00012-015-0358-8\">10.1007/s00012-015-0358-8</a>","ieee":"A. Kazda, “CSP for binary conservative relational structures,” <i>Algebra Universalis</i>, vol. 75, no. 1. Springer, pp. 75–84, 2016.","apa":"Kazda, A. (2016). CSP for binary conservative relational structures. <i>Algebra Universalis</i>. Springer. <a href=\"https://doi.org/10.1007/s00012-015-0358-8\">https://doi.org/10.1007/s00012-015-0358-8</a>","short":"A. Kazda, Algebra Universalis 75 (2016) 75–84.","chicago":"Kazda, Alexandr. “CSP for Binary Conservative Relational Structures.” <i>Algebra Universalis</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00012-015-0358-8\">https://doi.org/10.1007/s00012-015-0358-8</a>.","mla":"Kazda, Alexandr. “CSP for Binary Conservative Relational Structures.” <i>Algebra Universalis</i>, vol. 75, no. 1, Springer, 2016, pp. 75–84, doi:<a href=\"https://doi.org/10.1007/s00012-015-0358-8\">10.1007/s00012-015-0358-8</a>.","ista":"Kazda A. 2016. CSP for binary conservative relational structures. Algebra Universalis. 75(1), 75–84."},"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1112.1099"}],"volume":75,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer","day":"01","date_updated":"2025-09-18T11:00:04Z","author":[{"id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87","first_name":"Alexandr","last_name":"Kazda","full_name":"Kazda, Alexandr"}],"doi":"10.1007/s00012-015-0358-8","scopus_import":"1","year":"2016","oa":1,"external_id":{"arxiv":["1112.1099"],"isi":["000375422500006"]},"status":"public","page":"75 - 84","type":"journal_article","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:53:01Z"},{"title":"Synthetic discrete tomography problems","type":"research_data","has_accepted_license":"1","oa_version":"Published Version","doi":"10.15479/AT:ISTA:46","license":"https://creativecommons.org/publicdomain/zero/1.0/","oa":1,"year":"2016","status":"public","keyword":["discrete tomography"],"file_date_updated":"2020-07-14T12:47:02Z","date_created":"2018-12-12T12:31:31Z","contributor":[{"first_name":"Jan","last_name":"Kuske","contributor_type":"data_collector"}],"citation":{"ista":"Swoboda P. 2016. Synthetic discrete tomography problems, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:46\">10.15479/AT:ISTA:46</a>.","chicago":"Swoboda, Paul. “Synthetic Discrete Tomography Problems.” Institute of Science and Technology Austria, 2016. <a href=\"https://doi.org/10.15479/AT:ISTA:46\">https://doi.org/10.15479/AT:ISTA:46</a>.","mla":"Swoboda, Paul. <i>Synthetic Discrete Tomography Problems</i>. Institute of Science and Technology Austria, 2016, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:46\">10.15479/AT:ISTA:46</a>.","short":"P. Swoboda, (2016).","ama":"Swoboda P. Synthetic discrete tomography problems. 2016. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:46\">10.15479/AT:ISTA:46</a>","ieee":"P. Swoboda, “Synthetic discrete tomography problems.” Institute of Science and Technology Austria, 2016.","apa":"Swoboda, P. (2016). Synthetic discrete tomography problems. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:46\">https://doi.org/10.15479/AT:ISTA:46</a>"},"file":[{"relation":"main_file","file_id":"5645","file_size":36058401,"file_name":"IST-2016-46-v1+1_discrete_tomography_synthetic.zip","checksum":"aa5a16a0dc888da7186fb8fc45e88439","access_level":"open_access","date_updated":"2020-07-14T12:47:02Z","content_type":"application/zip","date_created":"2018-12-12T13:05:19Z","creator":"system"}],"_id":"5557","article_processing_charge":"No","datarep_id":"46","day":"20","tmp":{"short":"CC0 (1.0)","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","image":"/images/cc_0.png","name":"Creative Commons Public Domain Dedication (CC0 1.0)"},"date_updated":"2024-02-21T13:50:21Z","ddc":["006"],"author":[{"full_name":"Swoboda, Paul","last_name":"Swoboda","first_name":"Paul","id":"446560C6-F248-11E8-B48F-1D18A9856A87"}],"month":"09","date_published":"2016-09-20T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Small synthetic discrete tomography problems.\r\nSizes are 32x32, 64z64 and 256x256.\r\nProjection angles are 2, 4, and 6.\r\nNumber of labels are 3 and 5.","lang":"eng"}],"department":[{"_id":"VlKo"}],"publisher":"Institute of Science and Technology Austria"},{"publist_id":"5316","publication_status":"published","_id":"1794","ec_funded":1,"issue":"1","month":"09","date_published":"2016-09-01T00:00:00Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"abstract":[{"lang":"eng","text":"We consider Conditional random fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) (Formula presented.) is the sum of terms over intervals [i, j] where each term is non-zero only if the substring (Formula presented.) equals a prespecified pattern w. Such CRFs can be naturally applied to many sequence tagging problems. We present efficient algorithms for the three standard inference tasks in a CRF, namely computing (i) the partition function, (ii) marginals, and (iii) computing the MAP. Their complexities are respectively (Formula presented.), (Formula presented.) and (Formula presented.) where L is the combined length of input patterns, (Formula presented.) is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of Ye et al. (NIPS, 2009) whose complexities are respectively (Formula presented.), (Formula presented.) and (Formula presented.), where (Formula presented.) is the number of input patterns. In addition, we give an efficient algorithm for sampling, and revisit the case of MAP with non-positive weights."}],"related_material":{"record":[{"id":"2272","status":"public","relation":"earlier_version"}]},"department":[{"_id":"VlKo"}],"corr_author":"1","title":"Inference algorithms for pattern-based CRFs on sequence data","arxiv":1,"publication":"Algorithmica","oa_version":"Preprint","intvolume":"        76","quality_controlled":"1","isi":1,"citation":{"ista":"Kolmogorov V, Takhanov R. 2016. Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. 76(1), 17–46.","chicago":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” <i>Algorithmica</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00453-015-0017-7\">https://doi.org/10.1007/s00453-015-0017-7</a>.","mla":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” <i>Algorithmica</i>, vol. 76, no. 1, Springer, 2016, pp. 17–46, doi:<a href=\"https://doi.org/10.1007/s00453-015-0017-7\">10.1007/s00453-015-0017-7</a>.","short":"V. Kolmogorov, R. Takhanov, Algorithmica 76 (2016) 17–46.","apa":"Kolmogorov, V., &#38; Takhanov, R. (2016). Inference algorithms for pattern-based CRFs on sequence data. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/s00453-015-0017-7\">https://doi.org/10.1007/s00453-015-0017-7</a>","ieee":"V. Kolmogorov and R. Takhanov, “Inference algorithms for pattern-based CRFs on sequence data,” <i>Algorithmica</i>, vol. 76, no. 1. Springer, pp. 17–46, 2016.","ama":"Kolmogorov V, Takhanov R. Inference algorithms for pattern-based CRFs on sequence data. <i>Algorithmica</i>. 2016;76(1):17-46. doi:<a href=\"https://doi.org/10.1007/s00453-015-0017-7\">10.1007/s00453-015-0017-7</a>"},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1210.0508"}],"volume":76,"article_processing_charge":"No","date_updated":"2025-09-29T14:28:47Z","day":"01","author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Rustem","last_name":"Takhanov","id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87","full_name":"Takhanov, Rustem"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer","acknowledgement":"This work has been partially supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 616160.","type":"journal_article","page":"17 - 46","doi":"10.1007/s00453-015-0017-7","scopus_import":"1","oa":1,"year":"2016","status":"public","external_id":{"isi":["000381149500002"],"arxiv":["1210.0508"]},"date_created":"2018-12-11T11:54:02Z","language":[{"iso":"eng"}]},{"issue":"2","date_published":"2016-05-03T00:00:00Z","month":"05","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"abstract":[{"lang":"eng","text":"We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very effcient, offer a high degree of parallelism, and come along with memory requirements which are only in the order of the number of image pixels."}],"department":[{"_id":"VlKo"}],"publist_id":"5834","publication_status":"published","_id":"1377","ec_funded":1,"das_tickbox":"1","intvolume":"         9","quality_controlled":"1","citation":{"mla":"Kolmogorov, Vladimir, et al. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2, Society for Industrial and Applied Mathematics, 2016, pp. 605–36, doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>.","chicago":"Kolmogorov, Vladimir, Thomas Pock, and Michal Rolinek. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics, 2016. <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>.","ista":"Kolmogorov V, Pock T, Rolinek M. 2016. Total variation on a tree. SIAM Journal on Imaging Sciences. 9(2), 605–636.","ama":"Kolmogorov V, Pock T, Rolinek M. Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. 2016;9(2):605-636. doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>","ieee":"V. Kolmogorov, T. Pock, and M. Rolinek, “Total variation on a tree,” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2. Society for Industrial and Applied Mathematics, pp. 605–636, 2016.","apa":"Kolmogorov, V., Pock, T., &#38; Rolinek, M. (2016). Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>","short":"V. Kolmogorov, T. Pock, M. Rolinek, SIAM Journal on Imaging Sciences 9 (2016) 605–636."},"isi":1,"title":"Total variation on a tree","arxiv":1,"publication":"SIAM Journal on Imaging Sciences","oa_version":"Preprint","day":"03","date_updated":"2026-07-06T13:59:54Z","author":[{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov"},{"first_name":"Thomas","last_name":"Pock","full_name":"Pock, Thomas"},{"full_name":"Rolinek, Michal","first_name":"Michal","last_name":"Rolinek","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"url":"http://arxiv.org/abs/1502.07770","open_access":"1"}],"volume":9,"article_processing_charge":"No","date_created":"2018-12-11T11:51:40Z","language":[{"iso":"eng"}],"page":"605 - 636","type":"journal_article","doi":"10.1137/15M1010257","scopus_import":"1","year":"2016","oa":1,"external_id":{"isi":["000385275400005"],"arxiv":["1502.07770"]},"status":"public"},{"page":"1 - 36","type":"journal_article","scopus_import":"1","doi":"10.1137/130945648","external_id":{"isi":["000353967100001"],"arxiv":["1311.4219"]},"status":"public","year":"2015","oa":1,"date_created":"2018-12-11T11:56:41Z","language":[{"iso":"eng"}],"volume":44,"main_file_link":[{"url":"http://arxiv.org/abs/1311.4219","open_access":"1"}],"article_processing_charge":"No","date_updated":"2025-09-23T14:14:57Z","day":"01","author":[{"last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"full_name":"Thapper, Johan","first_name":"Johan","last_name":"Thapper"},{"last_name":"Živný","first_name":"Stanislav","full_name":"Živný, Stanislav"}],"publisher":"SIAM","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"The power of linear programming for general-valued CSPs","arxiv":1,"publication":"SIAM Journal on Computing","oa_version":"Preprint","intvolume":"        44","isi":1,"citation":{"chicago":"Kolmogorov, Vladimir, Johan Thapper, and Stanislav Živný. “The Power of Linear Programming for General-Valued CSPs.” <i>SIAM Journal on Computing</i>. SIAM, 2015. <a href=\"https://doi.org/10.1137/130945648\">https://doi.org/10.1137/130945648</a>.","mla":"Kolmogorov, Vladimir, et al. “The Power of Linear Programming for General-Valued CSPs.” <i>SIAM Journal on Computing</i>, vol. 44, no. 1, SIAM, 2015, pp. 1–36, doi:<a href=\"https://doi.org/10.1137/130945648\">10.1137/130945648</a>.","ista":"Kolmogorov V, Thapper J, Živný S. 2015. The power of linear programming for general-valued CSPs. SIAM Journal on Computing. 44(1), 1–36.","apa":"Kolmogorov, V., Thapper, J., &#38; Živný, S. (2015). The power of linear programming for general-valued CSPs. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/130945648\">https://doi.org/10.1137/130945648</a>","ieee":"V. Kolmogorov, J. Thapper, and S. Živný, “The power of linear programming for general-valued CSPs,” <i>SIAM Journal on Computing</i>, vol. 44, no. 1. SIAM, pp. 1–36, 2015.","ama":"Kolmogorov V, Thapper J, Živný S. The power of linear programming for general-valued CSPs. <i>SIAM Journal on Computing</i>. 2015;44(1):1-36. doi:<a href=\"https://doi.org/10.1137/130945648\">10.1137/130945648</a>","short":"V. Kolmogorov, J. Thapper, S. Živný, SIAM Journal on Computing 44 (2015) 1–36."},"quality_controlled":"1","publist_id":"4673","publication_status":"published","_id":"2271","issue":"1","month":"02","date_published":"2015-02-01T00:00:00Z","department":[{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. Finite-valued constraint languages contain functions that take on rational costs and general-valued constraint languages contain functions that take on rational or infinite costs. An instance of the problem is specified by a sum of functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs).\r\nOur main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a general-valued constraint language Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ, BLP is a decision procedure if and only if Γ admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism of arity 2.\r\nUsing these results, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. "}],"related_material":{"record":[{"id":"2518","status":"public","relation":"earlier_version"}]}},{"department":[{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism R→ΓΓ between two relational structures, e.g. between two directed graphs. Analyzing its complexity has been a prominent research direction, especially for the fixed template CSPs where the right side ΓΓ is fixed and the left side R is unconstrained.\r\n\r\nFar fewer results are known for the hybrid setting that restricts both sides simultaneously. It assumes that R belongs to a certain class of relational structures (called a structural restriction in this paper). We study which structural restrictions are effective, i.e. there exists a fixed template ΓΓ (from a certain class of languages) for which the problem is tractable when R is restricted, and NP-hard otherwise. We provide a characterization for structural restrictions that are closed under inverse homomorphisms. The criterion is based on the chromatic number of a relational structure defined in this paper; it generalizes the standard chromatic number of a graph.\r\n\r\nAs our main tool, we use the algebraic machinery developed for fixed template CSPs. To apply it to our case, we introduce a new construction called a “lifted language”. We also give a characterization for structural restrictions corresponding to minor-closed families of graphs, extend results to certain Valued CSPs (namely conservative valued languages), and state implications for (valued) CSPs with ordered variables and for the maximum weight independent set problem on some restricted families of graphs."}],"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"date_published":"2015-12-01T00:00:00Z","month":"12","publication_status":"published","publist_id":"5519","ec_funded":1,"_id":"1636","citation":{"chicago":"Kolmogorov, Vladimir, Michal Rolinek, and Rustem Takhanov. “Effectiveness of Structural Restrictions for Hybrid CSPs.” In <i>26th International Symposium</i>, 9472:566–77. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-662-48971-0_48\">https://doi.org/10.1007/978-3-662-48971-0_48</a>.","mla":"Kolmogorov, Vladimir, et al. “Effectiveness of Structural Restrictions for Hybrid CSPs.” <i>26th International Symposium</i>, vol. 9472, Springer Nature, 2015, pp. 566–77, doi:<a href=\"https://doi.org/10.1007/978-3-662-48971-0_48\">10.1007/978-3-662-48971-0_48</a>.","ista":"Kolmogorov V, Rolinek M, Takhanov R. 2015. Effectiveness of structural restrictions for hybrid CSPs. 26th International Symposium. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 9472, 566–577.","ama":"Kolmogorov V, Rolinek M, Takhanov R. Effectiveness of structural restrictions for hybrid CSPs. In: <i>26th International Symposium</i>. Vol 9472. Springer Nature; 2015:566-577. doi:<a href=\"https://doi.org/10.1007/978-3-662-48971-0_48\">10.1007/978-3-662-48971-0_48</a>","apa":"Kolmogorov, V., Rolinek, M., &#38; Takhanov, R. (2015). Effectiveness of structural restrictions for hybrid CSPs. In <i>26th International Symposium</i> (Vol. 9472, pp. 566–577). Nagoya, Japan: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-662-48971-0_48\">https://doi.org/10.1007/978-3-662-48971-0_48</a>","ieee":"V. Kolmogorov, M. Rolinek, and R. Takhanov, “Effectiveness of structural restrictions for hybrid CSPs,” in <i>26th International Symposium</i>, Nagoya, Japan, 2015, vol. 9472, pp. 566–577.","short":"V. Kolmogorov, M. Rolinek, R. Takhanov, in:, 26th International Symposium, Springer Nature, 2015, pp. 566–577."},"isi":1,"quality_controlled":"1","publication_identifier":{"isbn":["978-3-662-48970-3"]},"intvolume":"      9472","publication":"26th International Symposium","arxiv":1,"title":"Effectiveness of structural restrictions for hybrid CSPs","oa_version":"Preprint","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"},{"full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek"},{"first_name":"Rustem","last_name":"Takhanov","full_name":"Takhanov, Rustem"}],"day":"01","date_updated":"2025-09-23T08:39:38Z","publisher":"Springer Nature","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":9472,"main_file_link":[{"url":"http://arxiv.org/abs/1504.07067","open_access":"1"}],"article_processing_charge":"No","date_created":"2018-12-11T11:53:10Z","language":[{"iso":"eng"}],"alternative_title":["LNCS"],"type":"conference","page":"566 - 577","external_id":{"arxiv":["1504.07067"],"isi":["000375151300048"]},"status":"public","year":"2015","oa":1,"conference":{"end_date":"2015-12-11","name":"ISAAC: International Symposium on Algorithms and Computation","start_date":"2015-12-09","location":"Nagoya, Japan"},"scopus_import":"1","doi":"10.1007/978-3-662-48971-0_48"},{"department":[{"_id":"VlKo"}],"related_material":{"record":[{"id":"644","relation":"other","status":"public"}]},"abstract":[{"lang":"eng","text":"An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P ≠ NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one deals only with the feasibility issue and there is no optimization. This case is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which constraint languages CSPs are tractable (i.e. solvable in polynomial time) and for which NP-hard. The case when all allowed functions take only finite values corresponds to finite-valued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Zivny. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e. the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs."}],"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"date_published":"2015-12-01T00:00:00Z","month":"12","publist_id":"5518","publication_status":"published","ec_funded":1,"_id":"1637","citation":{"short":"V. Kolmogorov, A. Krokhin, M. Rolinek, in:, IEEE, 2015, pp. 1246–1258.","apa":"Kolmogorov, V., Krokhin, A., &#38; Rolinek, M. (2015). The complexity of general-valued CSPs (pp. 1246–1258). Presented at the FOCS: Foundations of Computer Science, Berkeley, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/FOCS.2015.80\">https://doi.org/10.1109/FOCS.2015.80</a>","ieee":"V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued CSPs,” presented at the FOCS: Foundations of Computer Science, Berkeley, CA, United States, 2015, pp. 1246–1258.","ama":"Kolmogorov V, Krokhin A, Rolinek M. The complexity of general-valued CSPs. In: IEEE; 2015:1246-1258. doi:<a href=\"https://doi.org/10.1109/FOCS.2015.80\">10.1109/FOCS.2015.80</a>","ista":"Kolmogorov V, Krokhin A, Rolinek M. 2015. The complexity of general-valued CSPs. FOCS: Foundations of Computer Science, 56th Annual Symposium on Foundations of Computer Science, , 1246–1258.","chicago":"Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity of General-Valued CSPs,” 1246–58. IEEE, 2015. <a href=\"https://doi.org/10.1109/FOCS.2015.80\">https://doi.org/10.1109/FOCS.2015.80</a>.","mla":"Kolmogorov, Vladimir, et al. <i>The Complexity of General-Valued CSPs</i>. IEEE, 2015, pp. 1246–58, doi:<a href=\"https://doi.org/10.1109/FOCS.2015.80\">10.1109/FOCS.2015.80</a>."},"isi":1,"quality_controlled":"1","title":"The complexity of general-valued CSPs","arxiv":1,"corr_author":"1","oa_version":"Preprint","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"},{"full_name":"Krokhin, Andrei","last_name":"Krokhin","first_name":"Andrei"},{"last_name":"Rolinek","first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal"}],"day":"01","date_updated":"2025-09-23T13:45:57Z","publisher":"IEEE","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1502.07327"}],"article_processing_charge":"No","date_created":"2018-12-11T11:53:10Z","alternative_title":["56th Annual Symposium on Foundations of Computer Science"],"language":[{"iso":"eng"}],"type":"conference","page":"1246 - 1258","status":"public","external_id":{"isi":["000379204700071"],"arxiv":["1502.07327"]},"year":"2015","conference":{"start_date":"2015-10-18","location":"Berkeley, CA, United States","name":"FOCS: Foundations of Computer Science","end_date":"2015-10-20"},"oa":1,"scopus_import":"1","doi":"10.1109/FOCS.2015.80"},{"title":"Proofs of space","publication":"35th Annual Cryptology Conference","oa_version":"Preprint","intvolume":"      9216","publication_identifier":{"isbn":["9783662479995"],"issn":["0302-9743"]},"quality_controlled":"1","isi":1,"citation":{"ista":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. 2015. Proofs of space. 35th Annual Cryptology Conference. CRYPTO: International Cryptology Conference, LNCS, vol. 9216, 585–605.","chicago":"Dziembowski, Stefan, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof Z Pietrzak. “Proofs of Space.” In <i>35th Annual Cryptology Conference</i>, 9216:585–605. Springer, 2015. <a href=\"https://doi.org/10.1007/978-3-662-48000-7_29\">https://doi.org/10.1007/978-3-662-48000-7_29</a>.","mla":"Dziembowski, Stefan, et al. “Proofs of Space.” <i>35th Annual Cryptology Conference</i>, vol. 9216, Springer, 2015, pp. 585–605, doi:<a href=\"https://doi.org/10.1007/978-3-662-48000-7_29\">10.1007/978-3-662-48000-7_29</a>.","short":"S. Dziembowski, S. Faust, V. Kolmogorov, K.Z. Pietrzak, in:, 35th Annual Cryptology Conference, Springer, 2015, pp. 585–605.","ama":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. Proofs of space. In: <i>35th Annual Cryptology Conference</i>. Vol 9216. Springer; 2015:585-605. doi:<a href=\"https://doi.org/10.1007/978-3-662-48000-7_29\">10.1007/978-3-662-48000-7_29</a>","ieee":"S. Dziembowski, S. Faust, V. Kolmogorov, and K. Z. Pietrzak, “Proofs of space,” in <i>35th Annual Cryptology Conference</i>, Santa Barbara, CA, United States, 2015, vol. 9216, pp. 585–605.","apa":"Dziembowski, S., Faust, S., Kolmogorov, V., &#38; Pietrzak, K. Z. (2015). Proofs of space. In <i>35th Annual Cryptology Conference</i> (Vol. 9216, pp. 585–605). Santa Barbara, CA, United States: Springer. <a href=\"https://doi.org/10.1007/978-3-662-48000-7_29\">https://doi.org/10.1007/978-3-662-48000-7_29</a>"},"pubrep_id":"671","publist_id":"5474","publication_status":"published","_id":"1675","ec_funded":1,"date_published":"2015-08-01T00:00:00Z","month":"08","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7"},{"call_identifier":"FP7","_id":"258C570E-B435-11E9-9278-68D0E5697425","grant_number":"259668","name":"Provable Security for Physical Cryptography"}],"related_material":{"record":[{"id":"2274","status":"public","relation":"earlier_version"}]},"abstract":[{"lang":"eng","text":"Proofs of work (PoW) have been suggested by Dwork and Naor (Crypto’92) as protection to a shared resource. The basic idea is to ask the service requestor to dedicate some non-trivial amount of computational work to every request. The original applications included prevention of spam and protection against denial of service attacks. More recently, PoWs have been used to prevent double spending in the Bitcoin digital currency system. In this work, we put forward an alternative concept for PoWs - so-called proofs of space (PoS), where a service requestor must dedicate a significant amount of disk space as opposed to computation. We construct secure PoS schemes in the random oracle model (with one additional mild assumption required for the proof to go through), using graphs with high “pebbling complexity” and Merkle hash-trees. We discuss some applications, including follow-up work where a decentralized digital currency scheme called Spacecoin is constructed that uses PoS (instead of wasteful PoW like in Bitcoin) to prevent double spending. The main technical contribution of this work is the construction of (directed, loop-free) graphs on N vertices with in-degree O(log logN) such that even if one places Θ(N) pebbles on the nodes of the graph, there’s a constant fraction of nodes that needs Θ(N) steps to be pebbled (where in every step one can put a pebble on a node if all its parents have a pebble)."}],"department":[{"_id":"VlKo"},{"_id":"KrPi"}],"page":"585 - 605","type":"conference","doi":"10.1007/978-3-662-48000-7_29","scopus_import":"1","conference":{"end_date":"2015-08-20","start_date":"2015-08-16","name":"CRYPTO: International Cryptology Conference","location":"Santa Barbara, CA, United States"},"year":"2015","oa":1,"external_id":{"isi":["000364183100029"]},"status":"public","date_created":"2018-12-11T11:53:24Z","alternative_title":["LNCS"],"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2013/796.pdf"}],"volume":9216,"article_processing_charge":"No","day":"01","date_updated":"2025-09-23T09:55:25Z","author":[{"first_name":"Stefan","last_name":"Dziembowski","full_name":"Dziembowski, Stefan"},{"last_name":"Faust","first_name":"Sebastian","full_name":"Faust, Sebastian"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"},{"last_name":"Pietrzak","first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer"},{"citation":{"mla":"Shah, Neel, et al. <i>A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly Max-Oracle</i>. IEEE, 2015, pp. 2737–45, doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7298890\">10.1109/CVPR.2015.7298890</a>.","chicago":"Shah, Neel, Vladimir Kolmogorov, and Christoph Lampert. “A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly Max-Oracle,” 2737–45. IEEE, 2015. <a href=\"https://doi.org/10.1109/CVPR.2015.7298890\">https://doi.org/10.1109/CVPR.2015.7298890</a>.","ista":"Shah N, Kolmogorov V, Lampert C. 2015. A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle. CVPR: Computer Vision and Pattern Recognition, 2737–2745.","apa":"Shah, N., Kolmogorov, V., &#38; Lampert, C. (2015). A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle (pp. 2737–2745). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. <a href=\"https://doi.org/10.1109/CVPR.2015.7298890\">https://doi.org/10.1109/CVPR.2015.7298890</a>","ieee":"N. Shah, V. Kolmogorov, and C. Lampert, “A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 2737–2745.","ama":"Shah N, Kolmogorov V, Lampert C. A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle. In: IEEE; 2015:2737-2745. doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7298890\">10.1109/CVPR.2015.7298890</a>","short":"N. Shah, V. Kolmogorov, C. Lampert, in:, IEEE, 2015, pp. 2737–2745."},"quality_controlled":"1","arxiv":1,"title":"A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle","corr_author":"1","oa_version":"Preprint","department":[{"_id":"VlKo"},{"_id":"ChLa"}],"abstract":[{"text":"Structural support vector machines (SSVMs) are amongst the best performing models for structured computer vision tasks, such as semantic image segmentation or human pose estimation. Training SSVMs, however, is computationally costly, because it requires repeated calls to a structured prediction subroutine (called \\emph{max-oracle}), which has to solve an optimization problem itself, e.g. a graph cut.\r\nIn this work, we introduce a new algorithm for SSVM training that is more efficient than earlier techniques when the max-oracle is computationally expensive, as it is frequently the case in computer vision tasks. The main idea is to (i) combine the recent stochastic Block-Coordinate Frank-Wolfe algorithm with efficient hyperplane caching, and (ii) use an automatic selection rule for deciding whether to call the exact max-oracle or to rely on an approximate one based on the cached hyperplanes.\r\nWe show experimentally that this strategy leads to faster convergence to the optimum with respect to the number of requires oracle calls, and that this translates into faster convergence with respect to the total runtime when the max-oracle is slow compared to the other steps of the algorithm. ","lang":"eng"}],"project":[{"name":"Lifelong Learning of Visual Scene Understanding","call_identifier":"FP7","grant_number":"308036","_id":"2532554C-B435-11E9-9278-68D0E5697425"},{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7"}],"date_published":"2015-06-01T00:00:00Z","month":"06","publist_id":"5240","publication_status":"published","ec_funded":1,"_id":"1859","date_created":"2018-12-11T11:54:24Z","language":[{"iso":"eng"}],"page":"2737 - 2745","type":"conference","external_id":{"arxiv":["1408.6804"]},"status":"public","conference":{"end_date":"2015-06-12","location":"Boston, MA, USA","start_date":"2015-06-07","name":"CVPR: Computer Vision and Pattern Recognition"},"oa":1,"year":"2015","scopus_import":"1","doi":"10.1109/CVPR.2015.7298890","author":[{"id":"31ABAF80-F248-11E8-B48F-1D18A9856A87","last_name":"Shah","first_name":"Neel","full_name":"Shah, Neel"},{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-8622-7887","first_name":"Christoph","last_name":"Lampert","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","full_name":"Lampert, Christoph"}],"day":"01","date_updated":"2025-06-11T07:20:12Z","publisher":"IEEE","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1408.6804"}],"article_processing_charge":"No"},{"oa":1,"year":"2015","status":"public","external_id":{"arxiv":["1309.5655"],"isi":["000352533000002"]},"doi":"10.1109/TPAMI.2014.2363465","scopus_import":"1","type":"journal_article","page":"919 - 930","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:54:18Z","OA_place":"repository","article_processing_charge":"No","main_file_link":[{"url":"http://arxiv.org/abs/1309.5655","open_access":"1"}],"volume":37,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"IEEE","author":[{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir"}],"OA_type":"green","date_updated":"2025-09-22T14:33:14Z","day":"01","oa_version":"Preprint","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","corr_author":"1","title":"A new look at reweighted message passing","arxiv":1,"quality_controlled":"1","isi":1,"citation":{"ama":"Kolmogorov V. A new look at reweighted message passing. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2015;37(5):919-930. doi:<a href=\"https://doi.org/10.1109/TPAMI.2014.2363465\">10.1109/TPAMI.2014.2363465</a>","apa":"Kolmogorov, V. (2015). A new look at reweighted message passing. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE. <a href=\"https://doi.org/10.1109/TPAMI.2014.2363465\">https://doi.org/10.1109/TPAMI.2014.2363465</a>","ieee":"V. Kolmogorov, “A new look at reweighted message passing,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 37, no. 5. IEEE, pp. 919–930, 2015.","short":"V. Kolmogorov, IEEE Transactions on Pattern Analysis and Machine Intelligence 37 (2015) 919–930.","chicago":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE, 2015. <a href=\"https://doi.org/10.1109/TPAMI.2014.2363465\">https://doi.org/10.1109/TPAMI.2014.2363465</a>.","mla":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 37, no. 5, IEEE, 2015, pp. 919–30, doi:<a href=\"https://doi.org/10.1109/TPAMI.2014.2363465\">10.1109/TPAMI.2014.2363465</a>.","ista":"Kolmogorov V. 2015. A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 37(5), 919–930."},"intvolume":"        37","ec_funded":1,"article_type":"original","_id":"1841","publication_status":"published","publist_id":"5261","abstract":[{"lang":"eng","text":"We propose a new family of message passing techniques for MAP estimation in graphical models which we call Sequential Reweighted Message Passing (SRMP). Special cases include well-known techniques such as Min-Sum Diffusion (MSD) and a faster Sequential Tree-Reweighted Message Passing (TRW-S). Importantly, our derivation is simpler than the original derivation of TRW-S, and does not involve a decomposition into trees. This allows easy generalizations. The new family of algorithms can be viewed as a generalization of TRW-S from pairwise to higher-order graphical models. We test SRMP on several real-world problems with promising results."}],"related_material":{"record":[{"id":"2273","status":"public","relation":"earlier_version"}]},"department":[{"_id":"VlKo"}],"date_published":"2015-05-01T00:00:00Z","month":"05","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"issue":"5"},{"publication_status":"published","publist_id":"4669","pubrep_id":"566","_id":"2275","department":[{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. \r\nThis partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. \r\nOur main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.\r\n"}],"month":"03","date_published":"2014-03-03T00:00:00Z","has_accepted_license":"1","title":"Partial enumeration and curvature regularization","oa_version":"Submitted Version","isi":1,"citation":{"ista":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. 2014. Partial enumeration and curvature regularization. ICCV: International Conference on Computer Vision, 2936–2943.","chicago":"Olsson, Carl, Johannes Ulen, Yuri Boykov, and Vladimir Kolmogorov. “Partial Enumeration and Curvature Regularization,” 2936–43. IEEE, 2014. <a href=\"https://doi.org/10.1109/ICCV.2013.365\">https://doi.org/10.1109/ICCV.2013.365</a>.","mla":"Olsson, Carl, et al. <i>Partial Enumeration and Curvature Regularization</i>. IEEE, 2014, pp. 2936–43, doi:<a href=\"https://doi.org/10.1109/ICCV.2013.365\">10.1109/ICCV.2013.365</a>.","short":"C. Olsson, J. Ulen, Y. Boykov, V. Kolmogorov, in:, IEEE, 2014, pp. 2936–2943.","ama":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. Partial enumeration and curvature regularization. In: IEEE; 2014:2936-2943. doi:<a href=\"https://doi.org/10.1109/ICCV.2013.365\">10.1109/ICCV.2013.365</a>","ieee":"C. Olsson, J. Ulen, Y. Boykov, and V. Kolmogorov, “Partial enumeration and curvature regularization,” presented at the ICCV: International Conference on Computer Vision, Sydney, Australia, 2014, pp. 2936–2943.","apa":"Olsson, C., Ulen, J., Boykov, Y., &#38; Kolmogorov, V. (2014). Partial enumeration and curvature regularization (pp. 2936–2943). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. <a href=\"https://doi.org/10.1109/ICCV.2013.365\">https://doi.org/10.1109/ICCV.2013.365</a>"},"quality_controlled":"1","article_processing_charge":"No","file":[{"file_size":378601,"file_id":"4754","relation":"main_file","date_created":"2018-12-12T10:09:30Z","content_type":"application/pdf","creator":"system","checksum":"4a74b5c92d6dcd2348c2c10ec8dd18bf","access_level":"open_access","date_updated":"2020-07-14T12:45:36Z","file_name":"IST-2016-566-v1+1_iccv13_part_enumeration.pdf"}],"author":[{"last_name":"Olsson","first_name":"Carl","full_name":"Olsson, Carl"},{"full_name":"Ulen, Johannes","first_name":"Johannes","last_name":"Ulen"},{"last_name":"Boykov","first_name":"Yuri","full_name":"Boykov, Yuri"},{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2025-09-29T14:28:16Z","day":"03","ddc":["000"],"publisher":"IEEE","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"conference","page":"2936 - 2943","external_id":{"isi":["000351830500367"]},"status":"public","oa":1,"year":"2014","conference":{"end_date":"2013-12-08","start_date":"2013-12-01","name":"ICCV: International Conference on Computer Vision","location":"Sydney, Australia"},"scopus_import":"1","doi":"10.1109/ICCV.2013.365","date_created":"2018-12-11T11:56:42Z","file_date_updated":"2020-07-14T12:45:36Z","language":[{"iso":"eng"}]},{"citation":{"ama":"Huszár K, Rolinek M. <i>Playful Math - An Introduction to Mathematical Games</i>. IST Austria","apa":"Huszár, K., &#38; Rolinek, M. (n.d.). <i>Playful Math - An introduction to mathematical games</i>. IST Austria.","ieee":"K. Huszár and M. Rolinek, <i>Playful Math - An introduction to mathematical games</i>. IST Austria.","short":"K. Huszár, M. Rolinek, Playful Math - An Introduction to Mathematical Games, IST Austria, n.d.","chicago":"Huszár, Kristóf, and Michal Rolinek. <i>Playful Math - An Introduction to Mathematical Games</i>. IST Austria, n.d.","mla":"Huszár, Kristóf, and Michal Rolinek. <i>Playful Math - An Introduction to Mathematical Games</i>. IST Austria.","ista":"Huszár K, Rolinek M. Playful Math - An introduction to mathematical games, IST Austria, 5p."},"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:48Z","date_created":"2019-11-18T15:57:05Z","oa_version":"Published Version","oa":1,"year":"2014","status":"public","corr_author":"1","title":"Playful Math - An introduction to mathematical games","page":"5","type":"working_paper","has_accepted_license":"1","month":"06","date_published":"2014-06-30T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"VlKo"},{"_id":"UlWa"}],"publisher":"IST Austria","date_updated":"2025-06-26T12:38:53Z","ddc":["510"],"day":"30","author":[{"full_name":"Huszár, Kristóf","id":"33C26278-F248-11E8-B48F-1D18A9856A87","first_name":"Kristóf","orcid":"0000-0002-5445-5057","last_name":"Huszár"},{"id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","first_name":"Michal","full_name":"Rolinek, Michal"}],"file":[{"file_size":511233,"file_id":"7039","relation":"main_file","date_updated":"2020-07-14T12:47:48Z","checksum":"2b94e5e1f4c3fe8ab89b12806276fb09","access_level":"open_access","creator":"dernst","content_type":"application/pdf","date_created":"2019-11-18T15:57:51Z","file_name":"2014_Playful_Math_Huszar.pdf"}],"article_processing_charge":"No","_id":"7038","publication_status":"draft"},{"date_published":"2013-12-31T00:00:00Z","month":"12","publisher":"AAAI Press","department":[{"_id":"VlKo"}],"abstract":[{"text":"Representation languages for coalitional games are a key research area in algorithmic game theory.   There is an inher-\r\nent tradeoff between how general a language is, allowing it to  capture  more  elaborate  games,  and  how  hard  it  is  computationally to optimize and solve such games.  One prominent  such  language  is  the  simple  yet  expressive\r\nWeighted Graph Games  (WGGs) representation (Deng  and Papadimitriou 1994), which maintains knowledge about synergies between agents in the form of an edge weighted graph. We  consider  the  problem  of  finding  the  optimal  coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We  show  that  finding  the  optimal  coalition  structure  is  not only hard for general graphs,  but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems.  We then provide algorithms with constant factor approximations for planar, minorfree and bounded degree graphs.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-07-10T11:52:18Z","day":"31","author":[{"first_name":"Yoram","last_name":"Bachrach","full_name":"Bachrach, Yoram"},{"last_name":"Kohli","first_name":"Pushmeet","full_name":"Kohli, Pushmeet"},{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"last_name":"Zadimoghaddam","first_name":"Morteza","full_name":"Zadimoghaddam, Morteza"}],"OA_type":"green","_id":"2270","article_processing_charge":"No","OA_place":"repository","publist_id":"4674","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/1108.5248","open_access":"1"}],"language":[{"iso":"eng"}],"citation":{"ista":"Bachrach Y, Kohli P, Kolmogorov V, Zadimoghaddam M. 2013. Optimal Coalition Structures in Cooperative Graph Games. AAAI: Conference on Artificial Intelligence, 81–87.","mla":"Bachrach, Yoram, et al. <i>Optimal Coalition Structures in Cooperative Graph Games</i>. AAAI Press, 2013, pp. 81–87.","chicago":"Bachrach, Yoram, Pushmeet Kohli, Vladimir Kolmogorov, and Morteza Zadimoghaddam. “Optimal Coalition Structures in Cooperative Graph Games,” 81–87. AAAI Press, 2013.","short":"Y. Bachrach, P. Kohli, V. Kolmogorov, M. Zadimoghaddam, in:, AAAI Press, 2013, pp. 81–87.","ama":"Bachrach Y, Kohli P, Kolmogorov V, Zadimoghaddam M. Optimal Coalition Structures in Cooperative Graph Games. In: AAAI Press; 2013:81-87.","ieee":"Y. Bachrach, P. Kohli, V. Kolmogorov, and M. Zadimoghaddam, “Optimal Coalition Structures in Cooperative Graph Games,” presented at the AAAI: Conference on Artificial Intelligence, Bellevue, WA, United States, 2013, pp. 81–87.","apa":"Bachrach, Y., Kohli, P., Kolmogorov, V., &#38; Zadimoghaddam, M. (2013). Optimal Coalition Structures in Cooperative Graph Games (pp. 81–87). Presented at the AAAI: Conference on Artificial Intelligence, Bellevue, WA, United States: AAAI Press."},"quality_controlled":"1","date_created":"2018-12-11T11:56:41Z","oa_version":"Preprint","external_id":{"arxiv":["1108.5248"]},"status":"public","year":"2013","conference":{"name":"AAAI: Conference on Artificial Intelligence","start_date":"2013-07-14","location":"Bellevue, WA, United States","end_date":"2013-07-18"},"oa":1,"arxiv":1,"title":"Optimal Coalition Structures in Cooperative Graph Games","type":"conference","page":"81-87"},{"main_file_link":[{"url":"http://proceedings.mlr.press/v28/takhanov13.pdf?CFID=105472548&CFTOKEN=5c5859b5d97b4439-27B4AC58-BA92-A964-B598CAACEE6CC515","open_access":"1"}],"volume":28,"article_processing_charge":"No","author":[{"id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87","first_name":"Rustem","last_name":"Takhanov","full_name":"Takhanov, Rustem"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"date_updated":"2025-09-29T14:28:48Z","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"ML Research Press","type":"conference","page":"145 - 153","conference":{"location":"Atlanta, GA, USA","start_date":"2013-06-16","name":"ICML: International Conference on Machine Learning","end_date":"2013-06-21"},"oa":1,"year":"2013","status":"public","external_id":{"isi":["000381149500002"]},"scopus_import":"1","date_created":"2018-12-11T11:56:41Z","alternative_title":["JMLR"],"language":[{"iso":"eng"}],"publication_status":"published","publist_id":"4672","_id":"2272","issue":"3","related_material":{"record":[{"id":"1794","status":"public","relation":"later_version"}]},"abstract":[{"lang":"eng","text":"We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) x1...xn is the sum of terms over intervals [i,j] where each term is non-zero only if the substring xi...xj equals a prespecified pattern α. Such CRFs can be naturally applied to many sequence tagging problems.\r\nWe present efficient algorithms for the three standard inference tasks in a CRF, namely computing (i) the partition function, (ii) marginals, and (iii) computing the MAP. Their complexities are respectively O(nL), O(nLℓmax) and O(nLmin{|D|,log(ℓmax+1)}) where L is the combined length of input patterns, ℓmax is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of (Ye et al., 2009) whose complexities are respectively O(nL|D|), O(n|Γ|L2ℓ2max) and O(nL|D|), where |Γ| is the number of input patterns.\r\nIn addition, we give an efficient algorithm for sampling. Finally, we consider the case of non-positive weights. (Komodakis &amp; Paragios, 2009) gave an O(nL) algorithm for computing the MAP. We present a modification that has the same worst-case complexity but can beat it in the best case. "}],"department":[{"_id":"VlKo"}],"month":"06","date_published":"2013-06-01T00:00:00Z","publication":"ICML'13 Proceedings of the 30th International Conference on International","corr_author":"1","title":"Inference algorithms for pattern-based CRFs on sequence data","oa_version":"Submitted Version","quality_controlled":"1","citation":{"short":"R. Takhanov, V. Kolmogorov, in:, ICML’13 Proceedings of the 30th International Conference on International, ML Research Press, 2013, pp. 145–153.","apa":"Takhanov, R., &#38; Kolmogorov, V. (2013). Inference algorithms for pattern-based CRFs on sequence data. In <i>ICML’13 Proceedings of the 30th International Conference on International</i> (Vol. 28, pp. 145–153). Atlanta, GA, USA: ML Research Press.","ieee":"R. Takhanov and V. Kolmogorov, “Inference algorithms for pattern-based CRFs on sequence data,” in <i>ICML’13 Proceedings of the 30th International Conference on International</i>, Atlanta, GA, USA, 2013, vol. 28, no. 3, pp. 145–153.","ama":"Takhanov R, Kolmogorov V. Inference algorithms for pattern-based CRFs on sequence data. In: <i>ICML’13 Proceedings of the 30th International Conference on International</i>. Vol 28. ML Research Press; 2013:145-153.","ista":"Takhanov R, Kolmogorov V. 2013. Inference algorithms for pattern-based CRFs on sequence data. ICML’13 Proceedings of the 30th International Conference on International. ICML: International Conference on Machine Learning, JMLR, vol. 28, 145–153.","chicago":"Takhanov, Rustem, and Vladimir Kolmogorov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” In <i>ICML’13 Proceedings of the 30th International Conference on International</i>, 28:145–53. ML Research Press, 2013.","mla":"Takhanov, Rustem, and Vladimir Kolmogorov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” <i>ICML’13 Proceedings of the 30th International Conference on International</i>, vol. 28, no. 3, ML Research Press, 2013, pp. 145–53."},"isi":1,"intvolume":"        28"},{"title":"Reweighted message passing revisited","arxiv":1,"corr_author":"1","type":"report","oa_version":"Preprint","status":"public","external_id":{"arxiv":["1309.5655"]},"oa":1,"year":"2013","date_created":"2018-12-11T11:56:42Z","citation":{"mla":"Kolmogorov, Vladimir. <i>Reweighted Message Passing Revisited</i>. IST Austria.","chicago":"Kolmogorov, Vladimir. <i>Reweighted Message Passing Revisited</i>. IST Austria, n.d.","ista":"Kolmogorov V. Reweighted message passing revisited, IST Austria,p.","ama":"Kolmogorov V. <i>Reweighted Message Passing Revisited</i>. IST Austria","ieee":"V. Kolmogorov, <i>Reweighted message passing revisited</i>. IST Austria.","apa":"Kolmogorov, V. (n.d.). <i>Reweighted message passing revisited</i>. IST Austria.","short":"V. Kolmogorov, Reweighted Message Passing Revisited, IST Austria, n.d."},"language":[{"iso":"eng"}],"publication_status":"draft","publist_id":"4671","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5655"}],"_id":"2273","article_processing_charge":"No","OA_place":"repository","date_updated":"2025-09-22T14:33:14Z","day":"22","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"month":"09","date_published":"2013-09-22T00:00:00Z","publisher":"IST Austria","department":[{"_id":"VlKo"}],"related_material":{"record":[{"id":"1841","status":"public","relation":"later_version"}]},"abstract":[{"text":"We propose a new family of message passing techniques for MAP estimation in graphical models which we call Sequential Reweighted Message Passing (SRMP). Special cases include well-known techniques such as Min-Sum Diusion (MSD) and a faster Sequential Tree-Reweighted Message Passing (TRW-S). Importantly, our derivation is simpler than the original derivation of TRW-S, and does not involve a  decomposition into trees. This allows easy generalizations. We present such a generalization for the case of higher-order graphical models, and test it on several real-world problems with promising results.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"pubrep_id":"671","publication_status":"published","publist_id":"4670","file":[{"file_name":"IST-2016-671-v1+1_796.pdf","date_updated":"2020-07-14T12:45:36Z","access_level":"open_access","checksum":"37b61637b62fc079d9141c59d9f1a94f","creator":"system","content_type":"application/pdf","date_created":"2018-12-12T10:16:11Z","file_id":"5197","relation":"main_file","file_size":405870}],"_id":"2274","author":[{"full_name":"Dziembowski, Stefan","first_name":"Stefan","last_name":"Dziembowski"},{"last_name":"Faust","first_name":"Sebastian","full_name":"Faust, Sebastian"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pietrzak, Krzysztof Z","first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87"}],"ddc":["530"],"day":"28","date_updated":"2025-09-23T09:55:25Z","abstract":[{"lang":"eng","text":"Proofs of work (PoW) have been suggested by Dwork and Naor (Crypto'92) as protection to a shared resource. The basic idea is to ask the service requestor to dedicate some non-trivial amount of computational work to every request. The original applications included prevention of spam and protection against denial of service attacks. More recently, PoWs have been used to prevent double spending in the Bitcoin digital currency system.\r\n\r\nIn this work, we put forward an alternative concept for PoWs -- so-called proofs of space (PoS), where a service requestor must dedicate a significant amount of disk space as opposed to computation. We construct secure PoS schemes in the random oracle model, using graphs with high &quot;pebbling complexity&quot; and Merkle hash-trees. "}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"1675","relation":"later_version","status":"public"}]},"publisher":"IST Austria","department":[{"_id":"VlKo"},{"_id":"KrPi"}],"date_published":"2013-11-28T00:00:00Z","month":"11","type":"report","has_accepted_license":"1","title":"Proofs of Space","year":"2013","oa":1,"status":"public","oa_version":"Published Version","scopus_import":1,"date_created":"2018-12-11T11:56:42Z","file_date_updated":"2020-07-14T12:45:36Z","citation":{"chicago":"Dziembowski, Stefan, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof Z Pietrzak. <i>Proofs of Space</i>. IST Austria, 2013.","mla":"Dziembowski, Stefan, et al. <i>Proofs of Space</i>. IST Austria, 2013.","ista":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. 2013. Proofs of Space, IST Austria,p.","ieee":"S. Dziembowski, S. Faust, V. Kolmogorov, and K. Z. Pietrzak, <i>Proofs of Space</i>. IST Austria, 2013.","apa":"Dziembowski, S., Faust, S., Kolmogorov, V., &#38; Pietrzak, K. Z. (2013). <i>Proofs of Space</i>. IST Austria.","ama":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. <i>Proofs of Space</i>. IST Austria; 2013.","short":"S. Dziembowski, S. Faust, V. Kolmogorov, K.Z. Pietrzak, Proofs of Space, IST Austria, 2013."},"language":[{"iso":"eng"}]},{"department":[{"_id":"JoCs"},{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19, 20]. It identifies a part of an optimal solution by running k maxflow computations, where k is the number of labels. The number of “labeled” pixels can be significant in some applications, e.g. 50-93% in our tests for stereo. We show how to reduce the runtime to O (log k) maxflow computations (or one parametric maxflow computation). Furthermore, the output of our algorithm allows to speed-up the subsequent alpha expansion for the unlabeled part, or can be used as it is for time-critical applications. To derive our technique, we generalize the algorithm of Felzenszwalb et al. [7] for Tree Metrics . We also show a connection to k-submodular functions from combinatorial optimization, and discuss k-submodular relaxations for general energy functions."}],"month":"12","date_published":"2013-12-01T00:00:00Z","publication_status":"published","publist_id":"4668","_id":"2276","isi":1,"citation":{"short":"I. Gridchyn, V. Kolmogorov, in:, IEEE, 2013, pp. 2320–2327.","ama":"Gridchyn I, Kolmogorov V. Potts model, parametric maxflow and k-submodular functions. In: IEEE; 2013:2320-2327. doi:<a href=\"https://doi.org/10.1109/ICCV.2013.288\">10.1109/ICCV.2013.288</a>","apa":"Gridchyn, I., &#38; Kolmogorov, V. (2013). Potts model, parametric maxflow and k-submodular functions (pp. 2320–2327). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. <a href=\"https://doi.org/10.1109/ICCV.2013.288\">https://doi.org/10.1109/ICCV.2013.288</a>","ieee":"I. Gridchyn and V. Kolmogorov, “Potts model, parametric maxflow and k-submodular functions,” presented at the ICCV: International Conference on Computer Vision, Sydney, Australia, 2013, pp. 2320–2327.","ista":"Gridchyn I, Kolmogorov V. 2013. Potts model, parametric maxflow and k-submodular functions. ICCV: International Conference on Computer Vision, 2320–2327.","mla":"Gridchyn, Igor, and Vladimir Kolmogorov. <i>Potts Model, Parametric Maxflow and k-Submodular Functions</i>. IEEE, 2013, pp. 2320–27, doi:<a href=\"https://doi.org/10.1109/ICCV.2013.288\">10.1109/ICCV.2013.288</a>.","chicago":"Gridchyn, Igor, and Vladimir Kolmogorov. “Potts Model, Parametric Maxflow and k-Submodular Functions,” 2320–27. IEEE, 2013. <a href=\"https://doi.org/10.1109/ICCV.2013.288\">https://doi.org/10.1109/ICCV.2013.288</a>."},"quality_controlled":"1","arxiv":1,"title":"Potts model, parametric maxflow and k-submodular functions","corr_author":"1","oa_version":"Preprint","author":[{"id":"4B60654C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1807-1929","first_name":"Igor","last_name":"Gridchyn","full_name":"Gridchyn, Igor"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"day":"01","date_updated":"2025-09-29T14:27:49Z","publisher":"IEEE","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.1771"}],"article_processing_charge":"No","date_created":"2018-12-11T11:56:43Z","language":[{"iso":"eng"}],"type":"conference","page":"2320 - 2327","external_id":{"arxiv":["1310.1771"],"isi":["000351830500290"]},"status":"public","year":"2013","oa":1,"conference":{"end_date":"2013-12-08","start_date":"2013-12-01","location":"Sydney, Australia","name":"ICCV: International Conference on Computer Vision"},"scopus_import":"1","doi":"10.1109/ICCV.2013.288"},{"intvolume":"      7965","citation":{"ista":"Kolmogorov V. 2013. The power of linear programming for finite-valued CSPs: A constructive characterization. ICALP: Automata, Languages and Programming, LNCS, vol. 7965, 625–636.","mla":"Kolmogorov, Vladimir. <i>The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization</i>. Vol. 7965, no. 1, Springer, 2013, pp. 625–36, doi:<a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">10.1007/978-3-642-39206-1_53</a>.","chicago":"Kolmogorov, Vladimir. “The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization,” 7965:625–36. Springer, 2013. <a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">https://doi.org/10.1007/978-3-642-39206-1_53</a>.","short":"V. Kolmogorov, in:, Springer, 2013, pp. 625–636.","ama":"Kolmogorov V. The power of linear programming for finite-valued CSPs: A constructive characterization. In: Vol 7965. Springer; 2013:625-636. doi:<a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">10.1007/978-3-642-39206-1_53</a>","apa":"Kolmogorov, V. (2013). The power of linear programming for finite-valued CSPs: A constructive characterization (Vol. 7965, pp. 625–636). Presented at the ICALP: Automata, Languages and Programming, Riga, Latvia: Springer. <a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">https://doi.org/10.1007/978-3-642-39206-1_53</a>","ieee":"V. Kolmogorov, “The power of linear programming for finite-valued CSPs: A constructive characterization,” presented at the ICALP: Automata, Languages and Programming, Riga, Latvia, 2013, vol. 7965, no. 1, pp. 625–636."},"quality_controlled":"1","title":"The power of linear programming for finite-valued CSPs: A constructive characterization","arxiv":1,"corr_author":"1","oa_version":"Preprint","issue":"1","date_published":"2013-07-01T00:00:00Z","month":"07","department":[{"_id":"VlKo"}],"abstract":[{"text":"A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard.","lang":"eng"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"2271"}]},"publist_id":"4383","publication_status":"published","_id":"2518","date_created":"2018-12-11T11:58:08Z","alternative_title":["LNCS"],"language":[{"iso":"eng"}],"type":"conference","page":"625 - 636","scopus_import":1,"doi":"10.1007/978-3-642-39206-1_53","status":"public","external_id":{"arxiv":["1207.7213"]},"year":"2013","oa":1,"conference":{"start_date":"2013-07-08","name":"ICALP: Automata, Languages and Programming","location":"Riga, Latvia","end_date":"2013-07-12"},"day":"01","date_updated":"2025-09-23T14:14:56Z","author":[{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"}],"publisher":"Springer","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":7965,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.7213"}]},{"quality_controlled":"1","citation":{"ista":"Kolmogorov V, Živný S. 2013. The complexity of conservative valued CSPs. Journal of the ACM. 60(2), 10.","chicago":"Kolmogorov, Vladimir, and Stanislav Živný. “The Complexity of Conservative Valued CSPs.” <i>Journal of the ACM</i>. ACM, 2013. <a href=\"https://doi.org/10.1145/2450142.2450146\">https://doi.org/10.1145/2450142.2450146</a>.","mla":"Kolmogorov, Vladimir, and Stanislav Živný. “The Complexity of Conservative Valued CSPs.” <i>Journal of the ACM</i>, vol. 60, no. 2, 10, ACM, 2013, doi:<a href=\"https://doi.org/10.1145/2450142.2450146\">10.1145/2450142.2450146</a>.","short":"V. Kolmogorov, S. Živný, Journal of the ACM 60 (2013).","ieee":"V. Kolmogorov and S. Živný, “The complexity of conservative valued CSPs,” <i>Journal of the ACM</i>, vol. 60, no. 2. ACM, 2013.","apa":"Kolmogorov, V., &#38; Živný, S. (2013). The complexity of conservative valued CSPs. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2450142.2450146\">https://doi.org/10.1145/2450142.2450146</a>","ama":"Kolmogorov V, Živný S. The complexity of conservative valued CSPs. <i>Journal of the ACM</i>. 2013;60(2). doi:<a href=\"https://doi.org/10.1145/2450142.2450146\">10.1145/2450142.2450146</a>"},"isi":1,"intvolume":"        60","publication":"Journal of the ACM","title":"The complexity of conservative valued CSPs","arxiv":1,"article_number":"10","oa_version":"Preprint","issue":"2","abstract":[{"lang":"eng","text":"We study the complexity of valued constraint satisfaction problems (VCSPs) parametrized by a constraint language, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum. Under the unique games conjecture, the approximability of finite-valued VCSPs is well understood, see Raghavendra [2008]. However, there is no characterization of finite-valued VCSPs, let alone general-valued VCSPs, that can be solved exactly in polynomial time, thus giving insights from a combinatorial optimization perspective. We consider the case of languages containing all possible unary cost functions. In the case of languages consisting of only {0, ∞}-valued cost functions (i.e., relations), such languages have been called conservative and studied by Bulatov [2003, 2011] and recently by Barto [2011]. Since we study valued languages, we call a language conservative if it contains all finite-valued unary cost functions. The computational complexity of conservative valued languages has been studied by Cohen et al. [2006] for languages over Boolean domains, by Deineko et al. [2008] for {0, 1}-valued languages (a.k.a Max-CSP), and by Takhanov [2010a] for {0, ∞}-valued languages containing all finite-valued unary cost functions (a.k.a. Min-Cost-Hom). We prove a Schaefer-like dichotomy theorem for conservative valued languages: if all cost functions in the language satisfy a certain condition (specified by a complementary combination of STP and MJN multimor-phisms), then any instance can be solved in polynomial time (via a new algorithm developed in this article), otherwise the language is NP-hard. This is the first complete complexity classification of general-valued constraint languages over non-Boolean domains. It is a common phenomenon that complexity classifications of problems over non-Boolean domains are significantly harder than the Boolean cases. The polynomial-time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of Cohen et al. [2008]. Our results generalize previous results by Takhanov [2010a] and (a subset of results) by Cohen et al. [2006] and Deineko et al. [2008]. Moreover, our results do not rely on any computer-assisted search as in Deineko et al. [2008], and provide a powerful tool for proving hardness of finite-valued and general-valued languages."}],"department":[{"_id":"VlKo"}],"month":"04","date_published":"2013-04-02T00:00:00Z","publication_status":"published","publist_id":"3971","_id":"2828","date_created":"2018-12-11T11:59:48Z","language":[{"iso":"eng"}],"type":"journal_article","year":"2013","oa":1,"status":"public","external_id":{"arxiv":["1110.2809"],"isi":["000318628500004"]},"doi":"10.1145/2450142.2450146","scopus_import":"1","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"},{"full_name":"Živný, Stanislav","last_name":"Živný","first_name":"Stanislav"}],"date_updated":"2025-09-29T13:52:07Z","day":"02","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"ACM","main_file_link":[{"url":"http://arxiv.org/abs/1110.2809","open_access":"1"}],"volume":60,"article_processing_charge":"No"},{"month":"01","date_published":"2013-01-01T00:00:00Z","abstract":[{"lang":"eng","text":" We introduce the M-modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook vectors for quantizing the configuration space, or they can form component centers for mixture model approximation. We present two algorithms for solving the M-modes problem. The first algorithm solves the problem in polynomial time when the underlying graphical model is a simple chain. The second algorithm solves the problem for junction chains. In synthetic and real dataset, we demonstrate how M-modes can improve the performance of prediction. We also use the generated modes as a tool to understand the topography of the probability distribution of configurations, for example with relation to the training set size and amount of noise in the data. "}],"department":[{"_id":"HeEd"},{"_id":"VlKo"},{"_id":"ChLa"}],"publist_id":"3846","publication_status":"published","_id":"2901","das_tickbox":"1","intvolume":"        31","quality_controlled":"1","citation":{"short":"C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, Proceedings of the 16th International Conference on Artificial Intelligence and Statistics, Journal of Machine Learning Research, 2013, pp. 161–169.","ama":"Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable modes of a graphical model. In: <i>Proceedings of the 16th International Conference on Artificial Intelligence and Statistics</i>. Vol 31. Journal of Machine Learning Research; 2013:161-169.","ieee":"C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the M most probable modes of a graphical model,” in <i>Proceedings of the 16th International Conference on Artificial Intelligence and Statistics</i>, Scottsdale, AZ, United States, 2013, vol. 31, pp. 161–169.","apa":"Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., &#38; Lampert, C. (2013). Computing the M most probable modes of a graphical model. In <i>Proceedings of the 16th International Conference on Artificial Intelligence and Statistics</i> (Vol. 31, pp. 161–169). Scottsdale, AZ, United States: Journal of Machine Learning Research.","ista":"Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M most probable modes of a graphical model. Proceedings of the 16th International Conference on Artificial Intelligence and Statistics. AISTATS: Conference on Uncertainty in Artificial Intelligence, PMLR, vol. 31, 161–169.","mla":"Chen, Chao, et al. “Computing the M Most Probable Modes of a Graphical Model.” <i>Proceedings of the 16th International Conference on Artificial Intelligence and Statistics</i>, vol. 31, Journal of Machine Learning Research, 2013, pp. 161–69.","chicago":"Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model.” In <i>Proceedings of the 16th International Conference on Artificial Intelligence and Statistics</i>, 31:161–69. Journal of Machine Learning Research, 2013."},"title":"Computing the M most probable modes of a graphical model","publication":"Proceedings of the 16th International Conference on Artificial Intelligence and Statistics","oa_version":"None","date_updated":"2026-07-06T13:43:58Z","day":"01","author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"},{"full_name":"Yan, Zhu","last_name":"Yan","first_name":"Zhu"},{"last_name":"Metaxas","first_name":"Dimitris","full_name":"Metaxas, Dimitris"},{"full_name":"Lampert, Christoph","last_name":"Lampert","first_name":"Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Journal of Machine Learning Research","main_file_link":[{"url":"http://jmlr.org/proceedings/papers/v31/chen13a.html","open_access":"1"}],"volume":31,"article_processing_charge":"No","date_created":"2018-12-11T12:00:14Z","language":[{"iso":"eng"}],"alternative_title":["PMLR"],"page":"161 - 169","type":"conference","scopus_import":"1","year":"2013","oa":1,"conference":{"end_date":"2013-05-01","location":"Scottsdale, AZ, United States","start_date":"2013-04-29","name":"AISTATS: Conference on Uncertainty in Artificial Intelligence"},"status":"public"}]