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Lipschitz Embeddings

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

Abstract

Let (X, d) be a finite semimetric space on n := |X| points. In general, (X, d) cannot be isometrically embedded into some 1-space. However, (X, d) admits always an embedding into some 1-space, where the distances are preserved up to a multiplicative factor whose size is of the order log n. This result is due to Bourgain [1985]. We present this result, together with an interesting application due to Linial, London and Rabinovich [1994] for approximating multicommodity flows. We also present a generalization of the negative type condition for Lipschitz 2-embeddings.

Keywords

Polynomial Time Positive Semidefinite Negative Type Multicommodity Flow Linear Programming Duality 
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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