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)


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.


Integer Program Valid Inequality Network Design Problem Separation Problem Submodular Function 
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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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