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Proofs of Space
TLDR
Proofs of work (PoW) have been suggested by Dwork and Naor as protection to a shared resource and used to prevent double spending in the Bitcoin digital currency system.
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On the Optimality of Tree-reweighted Max-product Message-passing
TLDR
This paper demonstrates how it is possible to identify part of the optimal solution—i.e., a provably optimal solution for a subset of nodes— without knowing a complete solution, and establishes that for submodular functions, a WTA fixed point always yields a globally optimal solution.
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A New Look at Reweighted Message Passing
  • V. Kolmogorov
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine…
  • 1 May 2015
TLDR
This work proposes a new family of message passing techniques for MAP estimation in graphical models which is simpler than the original derivation of TRW-S, and does not involve a decomposition into trees, which allows easy generalizations.
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Towards Minimizing k-Submodular Functions
TLDR
A k-submodular polyhedron is defined, a Min-Max-Theorem is proved, a greedy algorithm is given to construct the vertices of the polyhedrons, and the known Min- Max Theorem for submodular and bisubmodular functions is generalized.
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Minimizing a sum of submodular functions
  • V. Kolmogorov
  • Mathematics, Computer Science
    Discret. Appl. Math.
  • 10 June 2010
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Commutativity in the Algorithmic Lovász Local Lemma
  • V. Kolmogorov
  • Mathematics
    IEEE 57th Annual Symposium on Foundations of…
  • 29 June 2015
TLDR
A new "commutativity" condition is formulated, and it is proved that it is sufficient for an arbitrary rule to work, and enables an efficient parallelization under an additional assumption.
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Optimal Coalition Structure Generation in Cooperative Graph Games
TLDR
It is shown that finding the optimal coalition structure in WGGs 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.
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Total Variation on a Tree
TLDR
This work considers the problem of minimizing the continuous valued total variation subject to different unary terms on trees and proposes fast direct algorithms based on dynamic programming that are equal to or better than existing methods.
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The complexity of conservative valued CSPs
TLDR
A Schaefer-like dichotomy theorem is proved for conservative valued languages: if all cost functions in the language satisfy a certain condition, then any instance can be solved in polynomial time, otherwise the language is NP-hard.
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Computing the M Most Probable Modes of a Graphical Model
TLDR
This work introduces 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, and presents two algorithms for solving the MModes problem.
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