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