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Performance Guarantees for the TSP with a Parameterized Triangle Inequality

  • Michael A. Bender
  • Chandra Chekuri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

We consider the approximability of the TSP problem in graphs that satisfy a relaxed form of triangle inequality. More precisely, we assume that for some parameter τ ≥ 1, the distances satisfy the inequality dist(x,y) ≤τ. (dist(x,z)+ dist(z,y)) for every triple of vertices x, y, and z. We obtain a 4τ approximation and also show that for some > 0 it is NP-hard to obtain a (1 + ∈τ) approximation. Our upper bound improves upon the earlier known ratio of (3τ 2/2/+τ/2)[1] for all values of τ > 7/3.

Keywords

Triangle Inequality Minimum Span Tree Travel Salesman Problem Travel Salesman Problem Hamiltonian Cycle 
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 1999

Authors and Affiliations

  • Michael A. Bender
    • 1
  • Chandra Chekuri
    • 2
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA
  2. 2.Bell LaboratoriesMurray HillUSA

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