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Conditions for L1-Embeddability

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

Abstract

We present in this chapter two necessary conditions for L 1-embeddability, namely, the hypermetric and the negative type conditions. There are many other known necessary conditions, arising from the known valid inequalities for the cut cone; they will be described in Part V. We focus here on the hypermetric and negative type conditions. These conditions seem indeed to be among the most essential ones. For instance, there are several classes of distance spaces for which these conditions are also sufficient for ensuring L 1-embeddability; see, in particular, Chapters 8, 19, 24, and Remark 6.3.5 for a summary. Hypermetric inequalities will be treated in detail for their own sake in Part II and, as facets of the cut cone, in Chapter 28.

Keywords

Travel Salesman Problem Positive Semidefinite Positive Eigenvalue Distance Space Positive Type 
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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