Submodular Maximization by Simulated Annealing

We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [9] showed a 2/5-approximation for the unconstrained problem and also proved that no approximation better than 1/2 is possible in the value oracle model. Constant-factor approximation has been also known for submodular maximization subject to a matroid independence constraint (a factor of 0.309 [33]) and for submodular maximization subject to a matroid base constraint, provided that the fractional base packing number is bounded away from 1 (a 1/4-approximation assuming that 2 [33]). In this paper, we propose a new algorithm for submodular maximization which is based on the idea of simulated annealing. We prove that this algorithm achieves improved approximation for two problems: a 0.41-approximation for unconstrained submodular maximization, and a 0.325approximation for submodular maximization subject to a matroid independence constraint. On ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Shayan Oveis Gharan, Jan Vondrák
• Keywords: CORR 2010, Education, Matroid Independence Constraint, Submodular Maximization, Value Oracle Model