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Maximizing a Submodular Function by Integer Programming: A Polyhedral Approach

  • Heesang Lee
  • George L. Nemhauser
Conference paper
Part of the NATO ASI Series book series (volume 82)

Abstract

Let N = {1, 2,..., n} be a finite set. A real-valued function f whose domain is all of the subsets of N is said to be submodular if \(f\left( S \right) + f\left( T \right) \geqslant f\left( {S \cup T} \right) + f\left( {S \cap T} \right)for all S,T\).The problem of maximizing a submodular function includes many NP-hard combinatorial optimization problems, for example the max-cut problem, the uncapacitated facility location problem and some network design problems. Thus, this research is motivated by the opportunity of providing a unified approach to many NP-hard combinatorial optimization problems whose underlying structure is submodular.

Keywords

Integer Program Valid Inequality Network Design Problem Separation Problem Submodular Function 
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.

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Heesang Lee
  • George L. Nemhauser
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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