Oper. Res. Lett. | 2019
Constrained Submodular Maximization via Greedy Local Search
Abstract
We present a simple combinatorial $\\frac{1 -e^{-2}}{2}$-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. \nThis classic problem is known to be hard to approximate within factor better than $1 - 1/e$. We show that the algorithm can be extended to yield a ratio of $\\frac{1 - e^{-(k+1)}}{k+1}$ for the problem with a single knapsack and the intersection of $k$ matroid constraints, for any fixed $k > 1$. \nOur algorithms, which combine the greedy algorithm of [Khuller, Moss and Naor, 1999] and [Sviridenko, 2004] with local search, show the power of this natural framework in submodular maximization with combined constraints.