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)


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.


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