QUANTUM AND CLASSICAL ALGORITHMS FOR APPROXIMATE SUBMODULAR FUNCTION MINIMIZATION

摘要

Submodular functions are set functions mapping every subset of some ground set of size n into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory due to its relevance for various branches of mathematics, computer science and economics. The currently fastest strongly polynomial algorithm for exact minimization [1] runs in time (O) over tilde (n(3) center dot EO + n(4)) where EO denotes the cost to evaluate the function on any set. For functions with range [1], the best epsilon-additive approximation algorithm [2] runs in time (O) over tilde (n(5/3)/epsilon(2) center dot EO).