@techreport{2274,
abstract = {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, using graphs with high "pebbling complexity" and Merkle hash-trees. },
author = {Dziembowski, Stefan and Faust, Sebastian and Kolmogorov, Vladimir and Pietrzak, Krzysztof Z},
publisher = {IST Austria},
title = {{Proofs of Space}},
year = {2013},
}
@inproceedings{2276,
abstract = {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.},
author = {Gridchyn, Igor and Kolmogorov, Vladimir},
location = {Sydney, Australia},
pages = {2320 -- 2327},
publisher = {IEEE},
title = {{Potts model, parametric maxflow and k-submodular functions}},
doi = {10.1109/ICCV.2013.288},
year = {2013},
}
@inproceedings{2518,
abstract = {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.},
author = {Kolmogorov, Vladimir},
location = {Riga, Latvia},
number = {1},
pages = {625 -- 636},
publisher = {Springer},
title = {{The power of linear programming for finite-valued CSPs: A constructive characterization}},
doi = {10.1007/978-3-642-39206-1_53},
volume = {7965},
year = {2013},
}
@unpublished{2928,
abstract = { This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs of factors for which the marginalization constraint needs to be enforced. We develop a generalization of the TRW-S algorithm [9] for this problem, where we use a decomposition into junction chains, monotonic w.r.t. some ordering on the nodes. This generalizes the monotonic chains in [9] in a natural way. We also show how to deal with nested factors in an efficient way. Experiments show an improvement over min-sum diffusion, MPLP and subgradient ascent algorithms on a number of computer vision and natural language processing problems. },
author = {Kolmogorov, Vladimir and Schoenemann, Thomas},
booktitle = {arXiv},
pages = {16},
publisher = {ArXiv},
title = {{Generalized sequential tree-reweighted message passing}},
year = {2012},
}
@inproceedings{2930,
abstract = {In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively.
In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization problem over a (bi)submodular polyhedron. We define a k-submodular polyhedron, prove a Min-Max-Theorem for k-submodular functions, and give a greedy algorithm to construct the vertices of the polyhedron.
},
author = {Huber, Anna and Kolmogorov, Vladimir},
location = {Athens, Greece},
pages = {451 -- 462},
publisher = {Springer},
title = {{Towards minimizing k-submodular functions}},
doi = {10.1007/978-3-642-32147-4_40},
volume = {7422},
year = {2012},
}