Selected Applications of Minimum Cuts in Networks

This paper provides a review and a synthesis of applications of minimum cuts to a variety of combinatorial optimization problems, including linear and non-linear integer programming, problems in location theory, graph theory, sequencing and scheduling, and other areas. The central theme is a binary...

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Veröffentlicht in:INFOR. Information systems and operational research Jg. 20; H. 4; S. 394 - 422
Hauptverfasser: Picard, Jean-Claude, Queyranne, Maurice
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis 01.11.1982
ISSN:0315-5986, 1916-0615
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Abstract This paper provides a review and a synthesis of applications of minimum cuts to a variety of combinatorial optimization problems, including linear and non-linear integer programming, problems in location theory, graph theory, sequencing and scheduling, and other areas. The central theme is a binary quadratic programming formulation of the minimum cut problem. After reviewing alternative formulations, extensions, and direct applications ofminimum cuts in network problems, the problem of finding a closure with maximum weight ina directed graph is considered. This problem can be solved as a minimum cut problem, which allows other related problems to be solved as a sequence of minimum cut problems. The paper concludes by exploring more difficult versions of the minimum cut problem involving negative capacities or additional constraints.
AbstractList This paper provides a review and a synthesis of applications of minimum cuts to a variety of combinatorial optimization problems, including linear and non-linear integer programming, problems in location theory, graph theory, sequencing and scheduling, and other areas. The central theme is a binary quadratic programming formulation of the minimum cut problem. After reviewing alternative formulations, extensions, and direct applications ofminimum cuts in network problems, the problem of finding a closure with maximum weight ina directed graph is considered. This problem can be solved as a minimum cut problem, which allows other related problems to be solved as a sequence of minimum cut problems. The paper concludes by exploring more difficult versions of the minimum cut problem involving negative capacities or additional constraints.
Author Queyranne, Maurice
Picard, Jean-Claude
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  fullname: Queyranne, Maurice
  organization: University of Houston
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