On Approximating Multi-Criteria TSP
BODO MANTHEY, University of Twente
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem
First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman
problems (Max-TSP). For multi-criteria Max-STSP, where the edge weights have to be symmetric, we
devise an algorithm with an approximation ratio of 2/3 - . For multi-criteria Max-ATSP, where the edge
weights may be asymmetric, we present an algorithm with a ratio of 1/2 - . Our algorithms work for any
fixed number k of objectives. Furthermore, we present a deterministic algorithm for bi-criteria Max-STSP
that achieves an approximation ratio of 7/27.
Finally, we present a randomized approximation algorithm for the asymmetric multi-criteria minimum
TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of log n + .
Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Non-
numerical Algorithms and Problems
General Terms: Algorithms; Theory
Additional Key Words and Phrases: approximation algorithms, multi-criteria optimization, multiobjective
optimization, traveling salesman problem
ACM Reference Format:
ACM Trans. Algor. V, N, Article A ( YYYY), 18 pages.