[{"date_updated":"2023-10-17T09:51:31Z","date_created":"2018-12-11T11:54:02Z","volume":76,"author":[{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov"},{"id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87","first_name":"Rustem","last_name":"Takhanov","full_name":"Takhanov, Rustem"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"2272"}]},"publication_status":"published","department":[{"_id":"VlKo"}],"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.","year":"2016","ec_funded":1,"publist_id":"5316","language":[{"iso":"eng"}],"doi":"10.1007/s00453-015-0017-7","quality_controlled":"1","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1210.0508"}],"oa":1,"external_id":{"arxiv":["1210.0508"]},"month":"09","oa_version":"Preprint","status":"public","title":"Inference algorithms for pattern-based CRFs on sequence data","intvolume":" 76","_id":"1794","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"issue":"1","type":"journal_article","date_published":"2016-09-01T00:00:00Z","page":"17 - 46","publication":"Algorithmica","citation":{"mla":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” Algorithmica, vol. 76, no. 1, Springer, 2016, pp. 17–46, doi:10.1007/s00453-015-0017-7.","short":"V. Kolmogorov, R. Takhanov, Algorithmica 76 (2016) 17–46.","chicago":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” Algorithmica. Springer, 2016. https://doi.org/10.1007/s00453-015-0017-7.","ama":"Kolmogorov V, Takhanov R. Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. 2016;76(1):17-46. doi:10.1007/s00453-015-0017-7","ista":"Kolmogorov V, Takhanov R. 2016. Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. 76(1), 17–46.","apa":"Kolmogorov, V., & Takhanov, R. (2016). Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. Springer. https://doi.org/10.1007/s00453-015-0017-7","ieee":"V. Kolmogorov and R. Takhanov, “Inference algorithms for pattern-based CRFs on sequence data,” Algorithmica, vol. 76, no. 1. Springer, pp. 17–46, 2016."},"day":"01","scopus_import":1},{"date_published":"2016-09-20T00:00:00Z","doi":"10.15479/AT:ISTA:46","oa":1,"tmp":{"short":"CC0 (1.0)","image":"/images/cc_0.png","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","name":"Creative Commons Public Domain Dedication (CC0 1.0)"},"citation":{"apa":"Swoboda, P. (2016). Synthetic discrete tomography problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:46","ieee":"P. Swoboda, “Synthetic discrete tomography problems.” Institute of Science and Technology Austria, 2016.","ista":"Swoboda P. 2016. Synthetic discrete tomography problems, Institute of Science and Technology Austria, 10.15479/AT:ISTA:46.","ama":"Swoboda P. Synthetic discrete tomography problems. 2016. doi:10.15479/AT:ISTA:46","chicago":"Swoboda, Paul. “Synthetic Discrete Tomography Problems.” Institute of Science and Technology Austria, 2016. https://doi.org/10.15479/AT:ISTA:46.","short":"P. Swoboda, (2016).","mla":"Swoboda, Paul. Synthetic Discrete Tomography Problems. Institute of Science and Technology Austria, 2016, doi:10.15479/AT:ISTA:46."},"day":"20","month":"09","has_accepted_license":"1","article_processing_charge":"No","keyword":["discrete tomography"],"date_updated":"2024-02-21T13:50:21Z","date_created":"2018-12-12T12:31:31Z","oa_version":"Published Version","file":[{"checksum":"aa5a16a0dc888da7186fb8fc45e88439","date_updated":"2020-07-14T12:47:02Z","date_created":"2018-12-12T13:05:19Z","file_id":"5645","relation":"main_file","creator":"system","content_type":"application/zip","file_size":36058401,"access_level":"open_access","file_name":"IST-2016-46-v1+1_discrete_tomography_synthetic.zip"}],"author":[{"full_name":"Swoboda, Paul","first_name":"Paul","last_name":"Swoboda","id":"446560C6-F248-11E8-B48F-1D18A9856A87"}],"contributor":[{"first_name":"Jan","contributor_type":"data_collector","last_name":"Kuske"}],"ddc":["006"],"status":"public","title":"Synthetic discrete tomography problems","publisher":"Institute of Science and Technology Austria","department":[{"_id":"VlKo"}],"year":"2016","_id":"5557","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","license":"https://creativecommons.org/publicdomain/zero/1.0/","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"}],"file_date_updated":"2020-07-14T12:47:02Z","datarep_id":"46","type":"research_data"},{"oa_version":"Preprint","intvolume":" 9472","status":"public","title":"Effectiveness of structural restrictions for hybrid CSPs","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"1636","abstract":[{"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.","lang":"eng"}],"alternative_title":["LNCS"],"type":"conference","date_published":"2015-12-01T00:00:00Z","page":"566 - 577","citation":{"chicago":"Kolmogorov, Vladimir, Michal Rolinek, and Rustem Takhanov. “Effectiveness of Structural Restrictions for Hybrid CSPs.” In 26th International Symposium, 9472:566–77. Springer Nature, 2015. https://doi.org/10.1007/978-3-662-48971-0_48.","mla":"Kolmogorov, Vladimir, et al. “Effectiveness of Structural Restrictions for Hybrid CSPs.” 26th International Symposium, vol. 9472, Springer Nature, 2015, pp. 566–77, doi:10.1007/978-3-662-48971-0_48.","short":"V. Kolmogorov, M. Rolinek, R. Takhanov, in:, 26th International Symposium, Springer Nature, 2015, pp. 566–577.","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.","ieee":"V. Kolmogorov, M. Rolinek, and R. Takhanov, “Effectiveness of structural restrictions for hybrid CSPs,” in 26th International Symposium, Nagoya, Japan, 2015, vol. 9472, pp. 566–577.","apa":"Kolmogorov, V., Rolinek, M., & Takhanov, R. (2015). Effectiveness of structural restrictions for hybrid CSPs. In 26th International Symposium (Vol. 9472, pp. 566–577). Nagoya, Japan: Springer Nature. https://doi.org/10.1007/978-3-662-48971-0_48","ama":"Kolmogorov V, Rolinek M, Takhanov R. Effectiveness of structural restrictions for hybrid CSPs. In: 26th International Symposium. Vol 9472. Springer Nature; 2015:566-577. doi:10.1007/978-3-662-48971-0_48"},"publication":"26th International Symposium","article_processing_charge":"No","day":"01","scopus_import":"1","volume":9472,"date_created":"2018-12-11T11:53:10Z","date_updated":"2022-02-01T15:12:35Z","author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek","full_name":"Rolinek, Michal"},{"full_name":"Takhanov, Rustem","last_name":"Takhanov","first_name":"Rustem"}],"department":[{"_id":"VlKo"}],"publisher":"Springer Nature","publication_status":"published","year":"2015","publist_id":"5519","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-662-48971-0_48","conference":{"end_date":"2015-12-11","start_date":"2015-12-09","location":"Nagoya, Japan","name":"ISAAC: International Symposium on Algorithms and Computation"},"project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1504.07067"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1504.07067"}],"publication_identifier":{"isbn":["978-3-662-48970-3"]},"month":"12"},{"month":"05","quality_controlled":"1","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5655"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1109/TPAMI.2014.2363465","publist_id":"5261","ec_funded":1,"publication_status":"published","publisher":"IEEE","department":[{"_id":"VlKo"}],"year":"2015","date_created":"2018-12-11T11:54:18Z","date_updated":"2021-01-12T06:53:33Z","volume":37,"author":[{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":1,"day":"01","page":"919 - 930","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","citation":{"short":"V. Kolmogorov, IEEE Transactions on Pattern Analysis and Machine Intelligence 37 (2015) 919–930.","mla":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 5, IEEE, 2015, pp. 919–30, doi:10.1109/TPAMI.2014.2363465.","chicago":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2015. https://doi.org/10.1109/TPAMI.2014.2363465.","ama":"Kolmogorov V. A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2015;37(5):919-930. doi:10.1109/TPAMI.2014.2363465","apa":"Kolmogorov, V. (2015). A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/TPAMI.2014.2363465","ieee":"V. Kolmogorov, “A new look at reweighted message passing,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 5. IEEE, pp. 919–930, 2015.","ista":"Kolmogorov V. 2015. A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 37(5), 919–930."},"date_published":"2015-05-01T00:00:00Z","type":"journal_article","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."}],"issue":"5","title":"A new look at reweighted message passing","status":"public","intvolume":" 37","_id":"1841","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint"},{"author":[{"full_name":"Shah, Neel","id":"31ABAF80-F248-11E8-B48F-1D18A9856A87","last_name":"Shah","first_name":"Neel"},{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Lampert, Christoph","first_name":"Christoph","last_name":"Lampert","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8622-7887"}],"date_updated":"2021-01-12T06:53:40Z","date_created":"2018-12-11T11:54:24Z","oa_version":"Preprint","year":"2015","_id":"1859","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle","publication_status":"published","publisher":"IEEE","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"}],"ec_funded":1,"publist_id":"5240","type":"conference","conference":{"name":"CVPR: Computer Vision and Pattern Recognition","start_date":"2015-06-07","location":"Boston, MA, USA","end_date":"2015-06-12"},"date_published":"2015-06-01T00:00:00Z","doi":"10.1109/CVPR.2015.7298890","language":[{"iso":"eng"}],"oa":1,"citation":{"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:10.1109/CVPR.2015.7298890","apa":"Shah, N., Kolmogorov, V., & 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. https://doi.org/10.1109/CVPR.2015.7298890","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.","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.","short":"N. Shah, V. Kolmogorov, C. Lampert, in:, IEEE, 2015, pp. 2737–2745.","mla":"Shah, Neel, et al. A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly Max-Oracle. IEEE, 2015, pp. 2737–45, doi:10.1109/CVPR.2015.7298890.","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. https://doi.org/10.1109/CVPR.2015.7298890."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1408.6804"}],"quality_controlled":"1","project":[{"_id":"2532554C-B435-11E9-9278-68D0E5697425","grant_number":"308036","name":"Lifelong Learning of Visual Scene Understanding","call_identifier":"FP7"},{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"page":"2737 - 2745","day":"01","month":"06","scopus_import":1},{"quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1311.4219","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1311.4219"]},"language":[{"iso":"eng"}],"doi":"10.1137/130945648","month":"02","publication_status":"published","department":[{"_id":"VlKo"}],"publisher":"SIAM","year":"2015","date_updated":"2023-02-23T10:46:30Z","date_created":"2018-12-11T11:56:41Z","volume":44,"author":[{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov"},{"last_name":"Thapper","first_name":"Johan","full_name":"Thapper, Johan"},{"full_name":"Živný, Stanislav","last_name":"Živný","first_name":"Stanislav"}],"related_material":{"record":[{"id":"2518","relation":"earlier_version","status":"public"}]},"publist_id":"4673","page":"1 - 36","publication":"SIAM Journal on Computing","citation":{"apa":"Kolmogorov, V., Thapper, J., & Živný, S. (2015). The power of linear programming for general-valued CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/130945648","ieee":"V. Kolmogorov, J. Thapper, and S. Živný, “The power of linear programming for general-valued CSPs,” SIAM Journal on Computing, vol. 44, no. 1. SIAM, pp. 1–36, 2015.","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.","ama":"Kolmogorov V, Thapper J, Živný S. The power of linear programming for general-valued CSPs. SIAM Journal on Computing. 2015;44(1):1-36. doi:10.1137/130945648","chicago":"Kolmogorov, Vladimir, Johan Thapper, and Stanislav Živný. “The Power of Linear Programming for General-Valued CSPs.” SIAM Journal on Computing. SIAM, 2015. https://doi.org/10.1137/130945648.","short":"V. Kolmogorov, J. Thapper, S. Živný, SIAM Journal on Computing 44 (2015) 1–36.","mla":"Kolmogorov, Vladimir, et al. “The Power of Linear Programming for General-Valued CSPs.” SIAM Journal on Computing, vol. 44, no. 1, SIAM, 2015, pp. 1–36, doi:10.1137/130945648."},"date_published":"2015-02-01T00:00:00Z","scopus_import":1,"day":"01","title":"The power of linear programming for general-valued CSPs","status":"public","intvolume":" 44","_id":"2271","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","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. "}],"issue":"1"},{"month":"12","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1502.07327"}],"project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.1109/FOCS.2015.80","conference":{"end_date":"2015-10-20","location":"Berkeley, CA, United States","start_date":"2015-10-18","name":"FOCS: Foundations of Computer Science"},"language":[{"iso":"eng"}],"publist_id":"5518","ec_funded":1,"year":"2015","department":[{"_id":"VlKo"}],"publisher":"IEEE","publication_status":"published","related_material":{"record":[{"relation":"other","status":"public","id":"644"}]},"author":[{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"first_name":"Andrei","last_name":"Krokhin","full_name":"Krokhin, Andrei"},{"full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek"}],"date_updated":"2023-02-23T12:44:26Z","date_created":"2018-12-11T11:53:10Z","scopus_import":1,"day":"01","citation":{"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.","apa":"Kolmogorov, V., Krokhin, A., & 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. https://doi.org/10.1109/FOCS.2015.80","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:10.1109/FOCS.2015.80","chicago":"Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity of General-Valued CSPs,” 1246–58. IEEE, 2015. https://doi.org/10.1109/FOCS.2015.80.","mla":"Kolmogorov, Vladimir, et al. The Complexity of General-Valued CSPs. IEEE, 2015, pp. 1246–58, doi:10.1109/FOCS.2015.80.","short":"V. Kolmogorov, A. Krokhin, M. Rolinek, in:, IEEE, 2015, pp. 1246–1258."},"page":"1246 - 1258","date_published":"2015-12-01T00:00:00Z","type":"conference","alternative_title":["56th Annual Symposium on Foundations of Computer Science"],"abstract":[{"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.","lang":"eng"}],"_id":"1637","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The complexity of general-valued CSPs","status":"public","oa_version":"Preprint"},{"scopus_import":"1","day":"01","article_processing_charge":"No","page":"585 - 605","publication":"35th Annual Cryptology Conference","citation":{"short":"S. Dziembowski, S. Faust, V. Kolmogorov, K.Z. Pietrzak, in:, 35th Annual Cryptology Conference, Springer, 2015, pp. 585–605.","mla":"Dziembowski, Stefan, et al. “Proofs of Space.” 35th Annual Cryptology Conference, vol. 9216, Springer, 2015, pp. 585–605, doi:10.1007/978-3-662-48000-7_29.","chicago":"Dziembowski, Stefan, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof Z Pietrzak. “Proofs of Space.” In 35th Annual Cryptology Conference, 9216:585–605. Springer, 2015. https://doi.org/10.1007/978-3-662-48000-7_29.","ama":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. Proofs of space. In: 35th Annual Cryptology Conference. Vol 9216. Springer; 2015:585-605. doi:10.1007/978-3-662-48000-7_29","ieee":"S. Dziembowski, S. Faust, V. Kolmogorov, and K. Z. Pietrzak, “Proofs of space,” in 35th Annual Cryptology Conference, Santa Barbara, CA, United States, 2015, vol. 9216, pp. 585–605.","apa":"Dziembowski, S., Faust, S., Kolmogorov, V., & Pietrzak, K. Z. (2015). Proofs of space. In 35th Annual Cryptology Conference (Vol. 9216, pp. 585–605). Santa Barbara, CA, United States: Springer. https://doi.org/10.1007/978-3-662-48000-7_29","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."},"date_published":"2015-08-01T00:00:00Z","alternative_title":["LNCS"],"type":"conference","abstract":[{"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).","lang":"eng"}],"status":"public","title":"Proofs of space","intvolume":" 9216","_id":"1675","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","pubrep_id":"671","month":"08","publication_identifier":{"isbn":["9783662479995"],"issn":["0302-9743"]},"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"},{"grant_number":"259668","_id":"258C570E-B435-11E9-9278-68D0E5697425","name":"Provable Security for Physical Cryptography","call_identifier":"FP7"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2013/796.pdf"}],"language":[{"iso":"eng"}],"conference":{"name":"CRYPTO: International Cryptology Conference","location":"Santa Barbara, CA, United States","start_date":"2015-08-16","end_date":"2015-08-20"},"doi":"10.1007/978-3-662-48000-7_29","publist_id":"5474","ec_funded":1,"publication_status":"published","department":[{"_id":"VlKo"},{"_id":"KrPi"}],"publisher":"Springer","year":"2015","date_created":"2018-12-11T11:53:24Z","date_updated":"2024-03-20T08:31:49Z","volume":9216,"author":[{"last_name":"Dziembowski","first_name":"Stefan","full_name":"Dziembowski, Stefan"},{"last_name":"Faust","first_name":"Sebastian","full_name":"Faust, Sebastian"},{"last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","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"}],"related_material":{"record":[{"id":"2274","relation":"earlier_version","status":"public"}]}},{"_id":"2275","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Partial enumeration and curvature regularization","ddc":["000"],"pubrep_id":"566","oa_version":"Submitted Version","file":[{"file_id":"4754","relation":"main_file","date_created":"2018-12-12T10:09:30Z","date_updated":"2020-07-14T12:45:36Z","checksum":"4a74b5c92d6dcd2348c2c10ec8dd18bf","file_name":"IST-2016-566-v1+1_iccv13_part_enumeration.pdf","access_level":"open_access","creator":"system","file_size":378601,"content_type":"application/pdf"}],"type":"conference","abstract":[{"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","lang":"eng"}],"citation":{"short":"C. Olsson, J. Ulen, Y. Boykov, V. Kolmogorov, in:, IEEE, 2014, pp. 2936–2943.","mla":"Olsson, Carl, et al. Partial Enumeration and Curvature Regularization. IEEE, 2014, pp. 2936–43, doi:10.1109/ICCV.2013.365.","chicago":"Olsson, Carl, Johannes Ulen, Yuri Boykov, and Vladimir Kolmogorov. “Partial Enumeration and Curvature Regularization,” 2936–43. IEEE, 2014. https://doi.org/10.1109/ICCV.2013.365.","ama":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. Partial enumeration and curvature regularization. In: IEEE; 2014:2936-2943. doi:10.1109/ICCV.2013.365","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., & Kolmogorov, V. (2014). Partial enumeration and curvature regularization (pp. 2936–2943). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. https://doi.org/10.1109/ICCV.2013.365","ista":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. 2014. Partial enumeration and curvature regularization. ICCV: International Conference on Computer Vision, 2936–2943."},"page":"2936 - 2943","date_published":"2014-03-03T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"03","year":"2014","department":[{"_id":"VlKo"}],"publisher":"IEEE","publication_status":"published","author":[{"first_name":"Carl","last_name":"Olsson","full_name":"Olsson, Carl"},{"full_name":"Ulen, Johannes","first_name":"Johannes","last_name":"Ulen"},{"first_name":"Yuri","last_name":"Boykov","full_name":"Boykov, Yuri"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"date_updated":"2021-01-12T06:56:28Z","date_created":"2018-12-11T11:56:42Z","publist_id":"4669","file_date_updated":"2020-07-14T12:45:36Z","oa":1,"quality_controlled":"1","doi":"10.1109/ICCV.2013.365","conference":{"name":"ICCV: International Conference on Computer Vision","location":"Sydney, Australia","start_date":"2013-12-01","end_date":"2013-12-08"},"language":[{"iso":"eng"}],"month":"03"},{"file":[{"file_name":"2014_Playful_Math_Huszar.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":511233,"file_id":"7039","relation":"main_file","date_created":"2019-11-18T15:57:51Z","date_updated":"2020-07-14T12:47:48Z","checksum":"2b94e5e1f4c3fe8ab89b12806276fb09"}],"oa_version":"Published Version","date_created":"2019-11-18T15:57:05Z","date_updated":"2020-07-14T23:11:45Z","author":[{"first_name":"Kristóf","last_name":"Huszár","id":"33C26278-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5445-5057","full_name":"Huszár, Kristóf"},{"id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","first_name":"Michal","full_name":"Rolinek, Michal"}],"publisher":"IST Austria","department":[{"_id":"VlKo"},{"_id":"UlWa"}],"ddc":["510"],"title":"Playful Math - An introduction to mathematical games","status":"public","publication_status":"draft","_id":"7038","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2014","file_date_updated":"2020-07-14T12:47:48Z","type":"working_paper","language":[{"iso":"eng"}],"date_published":"2014-06-30T00:00:00Z","page":"5","citation":{"short":"K. Huszár, M. Rolinek, Playful Math - An Introduction to Mathematical Games, IST Austria, n.d.","mla":"Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction to Mathematical Games. IST Austria.","chicago":"Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction to Mathematical Games. IST Austria, n.d.","ama":"Huszár K, Rolinek M. Playful Math - An Introduction to Mathematical Games. IST Austria","apa":"Huszár, K., & Rolinek, M. (n.d.). Playful Math - An introduction to mathematical games. IST Austria.","ieee":"K. Huszár and M. Rolinek, Playful Math - An introduction to mathematical games. IST Austria.","ista":"Huszár K, Rolinek M. Playful Math - An introduction to mathematical games, IST Austria, 5p."},"oa":1,"has_accepted_license":"1","article_processing_charge":"No","day":"30","month":"06"}]