TY - GEN
T1 - Performance guarantees for the TSP with a parameterized triangle inequality
AU - Bender, Michael A.
AU - Chekuri, Chandra
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
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
UR - http://www.scopus.com/inward/citedby.url?scp=84948960900&partnerID=8YFLogxK
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 -