TY - GEN

T1 - Performance guarantees for the TSP with a parameterized triangle inequality

AU - Bender, Michael A.

AU - Chekuri, Chandra

N1 - Funding Information:
∗Corresponding author. Email: chekuri@research.bell-labs.com. 1 Email: bender@cs.sunysb.edu. Supported in part by ISX Corporation and Hughes Research Laboratories.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84948960900&partnerID=8YFLogxK

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U2 - 10.1007/3-540-48447-7_10

DO - 10.1007/3-540-48447-7_10

M3 - Conference contribution

AN - SCOPUS:84948960900

SN - 3540662790

SN - 9783540662792

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 80

EP - 85

BT - Algorithms and Data Structures - 6th International Workshop, WADS 1999, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Gupta, Arvind

A2 - Tamassia, Roberto

PB - Springer

T2 - 6th International Workshop on Algorithms and Data Structures, WADS 1999

Y2 - 11 August 1999 through 14 August 1999

ER -