An Optimal Approximation for Submodular Maximization Under a Matroid Constraint in the Adaptive Complexity Model

Abstract

An Exponentially Faster Algorithm for Submodular Maximization Under a Matroid Constraint This paper studies the problem of submodular maximization under a matroid constraint. It is known since the 1970s that the greedy algorithm obtains a constant-factor approximation guarantee for this problem. Twelve years ago, a breakthrough result by Vondrák obtained the optimal 1 − 1/e approximation. Previous algorithms for this fundamental problem all have linear parallel runtime, which was considered impossible to accelerate until recently. The main contribution of this paper is a novel algorithm that provides an exponential speedup in the parallel runtime of submodular maximization under a matroid constraint, without loss in the approximation guarantee.