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Nonmonotone Submodular Maximization via a Structural Continuous Greedy Algorithm

(Extended Abstract)
  • Moran Feldman
  • Joseph (Seffi) Naor
  • Roy Schwartz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

Consider a suboptimal solution S for a maximization problem. Suppose S’s value is small compared to an optimal solution OPT to the problem, yet S is structurally similar to OPT. A natural question in this setting is whether there is a way of improving S based solely on this information. In this paper we introduce the Structural Continuous Greedy Algorithm, answering this question affirmatively in the setting of the Nonmonotone Submodular Maximization Problem. We improve on the best approximation factor known for this problem. In the Nonmonotone Submodular Maximization Problem we are given a non-negative submodular function f, and the objective is to find a subset maximizing f. Our method yields an 0.42-approximation for this problem, improving on the current best approximation factor of 0.41 given by Gharan and Vondrák [5]. On the other hand, Feige et al. [4] showed a lower bound of 0.5 for this problem.

Keywords

IEEE Computer Society Simulated Annealing Algorithm Local Search Algorithm Submodular Function Annual IEEE Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Moran Feldman
    • 1
  • Joseph (Seffi) Naor
    • 1
  • Roy Schwartz
    • 1
  1. 1.Computer Science Dept.TechnionIsrael

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