A tight linear time (1/2)-approximation for unconstrained submodular maximization

Niv Buchbinder; Moran Feldman; Joseph Seffi Naor; Roy Schwartz

doi:10.1137/130929205

A tight linear time (1/2)-approximation for unconstrained submodular maximization

Niv Buchbinder, Moran Feldman, Joseph Seffi Naor, Roy Schwartz

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Unconstrained Submodular Maximization problem in which we are given a nonnegative submodular function f : 2^N → R⁺, and the objective is to find a subset S ⊆ N maximizing f(S). This is one of the most basic submodular optimization problems, having a wide range of applications. Some well-known problems captured by Unconstrained Submodular Maximization include Max-Cut, Max-DiCut, and variants of Max-SAT and maximum facility location. We present a simple randomized linear time algorithm achieving a tight approximation guarantee of 1/2, thus matching the known hardness result of Feige, Mirrokni, and Vondrák [SIAM J. Comput., 40 (2011), pp. 1133-1153]. Our algorithm is based on an adaptation of the greedy approach which exploits certain symmetry properties of the problem.

Original language	English
Pages (from-to)	1384-1402
Number of pages	19
Journal	SIAM Journal on Computing
Volume	44
Issue number	5
DOIs	https://doi.org/10.1137/130929205
State	Published - 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.

Keywords

Approximation algorithms
Linear time
Submodular functions

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10.1137/130929205

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A tight linear time (1/2)-approximation for unconstrained submodular maximization

Abstract

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Keywords

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