On Approximating Multi-Criteria TSP

Abstract. We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP), whose performances are independent of the number k of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present 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 that achieves an approximation ratio of 2/3 − ε. For multi-criteria Max-ATSP, where the edge weights may be asymmetric, we present an algorithm with an approximation ratio of 1/2 − ε. Our algorithms work for any fixed number k of objectives. To get these ratios, we introduce a decomposition technique for cycle covers. These decompositions are optimal in the sense that no decomposition can always yield more than a fraction of 2/3 and 1/2, respectively, of the weight of a cycle cover. Furthermore, ...

• Type: Conference
• Year: 2009
• Where: STACS
• Authors: Bodo Manthey
• Keywords: Algorithm, Approximation, Approximation Ratio, STACS 2009, Theoretical Computer Science