Approximation algorithms for multi-criteria traveling salesman problems

Abstract

We analyze approximation algorithms for several variants of the traveling salesman problem with multiple objective functions. First, we consider the symmetric TSP (STSP) with γ-triangle inequality. For this problem, we present a deterministic polynomial-time algorithm that achieves an approximation ratio of and a randomized approximation algorithm that achieves a ratio of. In particular, we obtain a 2+ε approximation for multi-criteria metric STSP. Then we show that multi-criteria cycle cover problems admit fully polynomial-time randomized approximation schemes. Based on these schemes, we present randomized approximation algorithms for STSP with γ-triangle inequality (ratio), asymmetric TSP (ATSP) with γ-triangle inequality (ratio), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2). © 2007 Springer Science+Business Media, LLC.