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Algorithms for a class of Min-Cut and Max-Cut problem

  • Teofilo F. Gonzalez
  • Toshio Murayama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

The k-Min-Cut (k-Max-Cut) problem consists of partitioning the vertices of an edge weighted (undirected) graph into k sets so as to minimize (maximize) the sum of the weights of the edges joining vertices in different subsets. We concentrate on the k-Max-Cut and k-Min-Cut problems defined over complete graphs that satisfy the triangle inequality, as well as on d-dimensional graphs. For the one-dimensional version of our partitioning problems, we present efficient algorithms for their solution as well as lower bounds for the time required to find an optimal solution, and for the time required to verify that a solution is an optimal one. We also establish a bound for the objective function value of an optimal solution to the k-Min-Cut and k-Max-Cut problems whose graph satisfies the triangle inequality. The existence of this bound is important because it implies that any feasible solution is a near-optimal approximation to such versions of the k-Max-Cut and k-Min-Cut problems.

Keywords

Triangle Inequality Time Algorithm Optimal Partition Linear Time Algorithm Verification Problem 
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 1992

Authors and Affiliations

  • Teofilo F. Gonzalez
    • 1
  • Toshio Murayama
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Sony Corporation System LSI GroupKanagawaJapan

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