@inproceedings{916, abstract = {We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore this direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art anytime solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each.}, author = {Swoboda, Paul and Rother, Carsten and Abu Alhaija, Carsten and Kainmueller, Dagmar and Savchynskyy, Bogdan}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {7062--7071}, publisher = {IEEE}, title = {{A study of lagrangean decompositions and dual ascent solvers for graph matching}}, doi = {10.1109/CVPR.2017.747}, volume = {2017}, year = {2017}, } @inproceedings{915, abstract = {We propose a dual decomposition and linear program relaxation of the NP-hard minimum cost multicut problem. Unlike other polyhedral relaxations of the multicut polytope, it is amenable to efficient optimization by message passing. Like other polyhedral relaxations, it can be tightened efficiently by cutting planes. We define an algorithm that alternates between message passing and efficient separation of cycle- and odd-wheel inequalities. This algorithm is more efficient than state-of-the-art algorithms based on linear programming, including algorithms written in the framework of leading commercial software, as we show in experiments with large instances of the problem from applications in computer vision, biomedical image analysis and data mining.}, author = {Swoboda, Paul and Andres, Bjoern}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {4990--4999}, publisher = {IEEE}, title = {{A message passing algorithm for the minimum cost multicut problem}}, doi = {10.1109/CVPR.2017.530}, volume = {2017}, year = {2017}, } @inproceedings{917, abstract = {We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In this work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers.}, author = {Swoboda, Paul and Kuske, Jan and Savchynskyy, Bogdan}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {4950--4960}, publisher = {IEEE}, title = {{A dual ascent framework for Lagrangean decomposition of combinatorial problems}}, doi = {10.1109/CVPR.2017.526}, volume = {2017}, year = {2017}, } @inproceedings{274, abstract = {We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings of the 31st Conference On Learning Theory}, pages = {228--249}, publisher = {ML Research Press}, title = {{A faster approximation algorithm for the Gibbs partition function}}, volume = {75}, year = {2017}, } @misc{5561, abstract = {Graph matching problems as described in "Active Graph Matching for Automatic Joint Segmentation and Annotation of C. Elegans." by Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Myers, Gene, MICCAI 2014. Problems are in OpenGM2 hdf5 format (see http://hciweb2.iwr.uni-heidelberg.de/opengm/) and a custom text format used by the feature matching solver described in "Feature Correspondence via Graph Matching: Models and Global Optimization." by Lorenzo Torresani, Vladimir Kolmogorov and Carsten Rother, ECCV 2008, code at http://pub.ist.ac.at/~vnk/software/GraphMatching-v1.02.src.zip. }, author = {Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Meyers, Gene}, keywords = {graph matching, feature matching, QAP, MAP-inference}, publisher = {Institute of Science and Technology Austria}, title = {{Graph matching problems for annotating C. Elegans}}, doi = {10.15479/AT:ISTA:57}, year = {2017}, } @inproceedings{1231, abstract = {We study the time-and memory-complexities of the problem of computing labels of (multiple) randomly selected challenge-nodes in a directed acyclic graph. The w-bit label of a node is the hash of the labels of its parents, and the hash function is modeled as a random oracle. Specific instances of this problem underlie both proofs of space [Dziembowski et al. CRYPTO’15] as well as popular memory-hard functions like scrypt. As our main tool, we introduce the new notion of a probabilistic parallel entangled pebbling game, a new type of combinatorial pebbling game on a graph, which is closely related to the labeling game on the same graph. As a first application of our framework, we prove that for scrypt, when the underlying hash function is invoked n times, the cumulative memory complexity (CMC) (a notion recently introduced by Alwen and Serbinenko (STOC’15) to capture amortized memory-hardness for parallel adversaries) is at least Ω(w · (n/ log(n))2). This bound holds for adversaries that can store many natural functions of the labels (e.g., linear combinations), but still not arbitrary functions thereof. We then introduce and study a combinatorial quantity, and show how a sufficiently small upper bound on it (which we conjecture) extends our CMC bound for scrypt to hold against arbitrary adversaries. We also show that such an upper bound solves the main open problem for proofs-of-space protocols: namely, establishing that the time complexity of computing the label of a random node in a graph on n nodes (given an initial kw-bit state) reduces tightly to the time complexity for black pebbling on the same graph (given an initial k-node pebbling).}, author = {Alwen, Joel F and Chen, Binyi and Kamath Hosdurg, Chethan and Kolmogorov, Vladimir and Pietrzak, Krzysztof Z and Tessaro, Stefano}, location = {Vienna, Austria}, pages = {358 -- 387}, publisher = {Springer}, title = {{On the complexity of scrypt and proofs of space in the parallel random oracle model}}, doi = {10.1007/978-3-662-49896-5_13}, volume = {9666}, year = {2016}, } @article{1353, abstract = {We characterize absorption in finite idempotent algebras by means of Jónsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations.}, author = {Barto, Libor and Kazda, Alexandr}, journal = {International Journal of Algebra and Computation}, number = {5}, pages = {1033 -- 1060}, publisher = {World Scientific Publishing}, title = {{Deciding absorption}}, doi = {10.1142/S0218196716500430}, volume = {26}, year = {2016}, } @article{1377, abstract = {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.}, author = {Kolmogorov, Vladimir and Pock, Thomas and Rolinek, Michal}, journal = {SIAM Journal on Imaging Sciences}, number = {2}, pages = {605 -- 636}, publisher = {Society for Industrial and Applied Mathematics }, title = {{Total variation on a tree}}, doi = {10.1137/15M1010257}, volume = {9}, year = {2016}, } @article{1612, abstract = {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).}, author = {Kazda, Alexandr}, journal = {Algebra Universalis}, number = {1}, pages = {75 -- 84}, publisher = {Springer}, title = {{CSP for binary conservative relational structures}}, doi = {10.1007/s00012-015-0358-8}, volume = {75}, year = {2016}, } @inproceedings{1193, abstract = {We consider the recent formulation of the Algorithmic Lovász Local Lemma [1], [2] for finding objects that avoid "bad features", or "flaws". It extends the Moser-Tardos resampling algorithm [3] to more general discrete spaces. At each step the method picks a flaw present in the current state and "resamples" it using a "resampling oracle" provided by the user. However, it is less flexible than the Moser-Tardos method since [1], [2] require a specific flaw selection rule, whereas [3] allows an arbitrary rule (and thus can potentially be implemented more efficiently). We formulate a new "commutativity" condition, and prove that it is sufficient for an arbitrary rule to work. It also enables an efficient parallelization under an additional assumption. We then show that existing resampling oracles for perfect matchings and permutations do satisfy this condition. Finally, we generalize the precondition in [2] (in the case of symmetric potential causality graphs). This unifies special cases that previously were treated separately.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings - Annual IEEE Symposium on Foundations of Computer Science}, location = {New Brunswick, NJ, USA }, publisher = {IEEE}, title = {{Commutativity in the algorithmic Lovasz local lemma}}, doi = {10.1109/FOCS.2016.88}, volume = {2016-December}, year = {2016}, }