Minimum Entropy Combinatorial Optimization Problems

TL;DR: This work surveys recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution, including the minimum entropy set cover, minimum entropy orientation, and minimum entropy coloring problems.

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: This work outlines results and open problems concerning partitioning of integer sequences and partial orders into heapable subsequences (previously defined and established by Byers et al.).

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: 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.

TL;DR: This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data.