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

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

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


We consider the Unconstrained Sub modular Maximization problem in which we are given a non-negative sub modular function f:2N → ℝ+, and the objective is to find a subset S ⊆ N maximizing f(S). This is one of the most basic sub modular optimization problems, having a wide range of applications. Some well known problems captured by Unconstrained Sub modular 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 et al. Our algorithm is based on an adaptation of the greedy approach which exploits certain symmetry properties of the problem. Our method might seem counterintuitive, since it is known that the greedy algorithm fails to achieve any bounded approximation factor for the problem.

Original languageEnglish
Article number6375344
Pages (from-to)649-658
Number of pages10
JournalProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
StatePublished - 2012
Event53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012 - New Brunswick, NJ, United States
Duration: 20 Oct 201223 Oct 2012


  • Approximation Algorithms
  • Submodular Functions


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