Nearly Linear-Time, Deterministic Algorithm for Maximizing (Non-Monotone) Submodular Functions Under Cardinality Constraint

02/17/2019

∙

by   Alan Kuhnle, et al.

∙

0

∙

share

A deterministic, nearly linear-time, approximation algorithm FastInterlaceGreedy is developed, for the maximization of non-monotone submodular functions under cardinality constraint. The approximation ratio of 1/4 - ε is an improvement over the next fastest deterministic algorithm for this problem, which requires quadratic time to achieve ratio 1/6 - ε. The algorithm FastInterlaceGreedy is a novel interlacing of multiple greedy procedures and is validated in the context of two applications, on which FastInterlaceGreedy outperforms the fastest deterministic and randomized algorithms in prior literature.