Maximizing Non-Monotone Submodular Functions

Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard. In this paper, we design the first constant-factor approximation algorithms for maximizing nonnegative submodular functions. In particular, we give a deterministic local search 1 3 -approximation and a randomized 2 5 -approximation algorithm for maximizing nonnegative submodular functions. We also show that a uniformly random set gives a 1 4 approximation. For symmetric submodular functions, we show that a random set gives a 1 2 -approximation, which can be also achieved by deterministic local search. These algorithms work in the value oracle model where the submodular function is accessible through a black box returning f(S) for a given set S. We show that in this mode...

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Uriel Feige, Vahab S. Mirrokni, Jan Vondrák
• Keywords: FOCS 2007, Nonnegative Submodular Functions, Submodular Functions, Symmetric Submodular Functions, Theoretical Computer Science