Constrained submodular maximization via greedy local search

被引：21

作者：

Sarpatwar, Kanthi K. ^{[1
]}

Schieber, Baruch ^{[2
]}

Shachnai, Hadas ^{[3
]}

机构：

[1] IBM TJ Watson Res Ctr, Yorktown Hts, NY 10598 USA

[2] New Jersey Inst Technol, Dept Comp Sci, Newark, NJ 07102 USA

[3] Technion, Comp Sci Dept, IL-3200003 Haifa, Israel

来源：

OPERATIONS RESEARCH LETTERS | 2019年 / 47卷 / 01期

基金：

美国国家科学基金会;

关键词：

Submodular functions; Matroid; Knapsack; APPROXIMATIONS;

D O I：

10.1016/j.orl.2018.11.002

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We present a simple combinatorial 1-e(-2)/2 approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is knownto be hard to approximate within factor better than 1 - 1/e. We extend the algorithm to yield 1-e(-(k+1))/k+1 approximation for submodular maximization subject to a single knapsack and k matroid constraints, for any fixed k > 1. Our algorithms, which combine the greedy algorithm of Khuller et al. (1999) and Sviridenko (2004) with local search, show the power of this natural framework in submodular maximization with combined constraints. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1 / 6

页数：6

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