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Hypermetric Inequalities

  • Michel Marie Deza
  • Monique Laurent
Part of the Algorithms and Combinatorics book series (AC, volume 15)

Abstract

In this chapter we study in detail the class of hypermetric inequalities. In partic­ular, we present several subclasses of hypermetric inequalities that define facets of the cut cone. We also address the separation problem for hypermetric in­equalities. Although its exact complexity status is not known, there are several results that indicate that it is very likely to be a hard problem. In particular, the problem of finding the smallest violated hypermetric inequality is NP-hard.

Keywords

Convex Body Positive Semidefinite Valid Inequality Separation Problem Positive Semidefinite Matrix 
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 1997

Authors and Affiliations

  • Michel Marie Deza
    • 1
    • 2
  • Monique Laurent
    • 1
    • 3
  1. 1.Département de Mathématiques et d’InformatiqueLaboratoire d’Informatique de l’Ecole Normale SupérieureParis Cedex 05France
  2. 2.Department of MathematicsMoscow Pedagogical State UniversityMoscowRussia
  3. 3.CWIAmsterdamThe Netherlands

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