Minimum Entropy Combinatorial Optimization Problems

TL;DR: Some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals and the notion of minimum entropy coupling is introduced and its relevance is demonstrated in information-theoretic, computational, and statistical contexts.

TL;DR: The authors propose a high-speed chance-constrained programming method by aggregating the constraints that are generated by approximation of the problem in the sample average method and confirmed that computational time is decreased to 1 min while obtaining the same error rate and the same rate of feasible solutions as a conventional method.

TL;DR: A general algorithmic solution based on solving the problem variant without the cardinality constraint is presented and constant factor approximations depending on the solvability of this relaxation are obtained for a large class of submodular cost functions which are called value-monotone sub modular functions.

TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.

TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.

TL;DR: The Strong Perfect Graph Conjecture as discussed by the authors is based on the strong perfect graph conjecture, which is a generalization of the concept of generalized perfection, generalized perfection and related concepts.