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arXiv · 1705.06319

Constrained Submodular Maximization via Greedy Local Search

Kanthi K. Sarpatwar·Baruch Schieber·Hadas Shachnai
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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. This 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 $k > 1$. Our 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.

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Kanthi K. Sarpatwar, Baruch Schieber, Hadas Shachnai. 2017-05-17. Constrained Submodular Maximization via Greedy Local Search. https://arxiv.org/abs/1705.06319

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