Improved and Derandomized Approximations for Two-Criteria Metric Traveling Salesman

We improve and derandomize the best known approximation algorithm for the twocriteria metric traveling salesman problem (2-TSP). More precisely, we construct a deterministic 2-approximation which answers an open question by Manthey. Moreover, we show that 2-TSP is randomized (3=2 + "; 2)-approximable, and we give the rst randomized approximations for the two-criteria traveling salesman path problems 2-TSPP, 2-TSPPs, and 2-TSPPst. We further provide arguments that indicate the hardness of improving our randomized approximation algorithms in the sense that such improvements force us to improve the best known approximations for TSP, TSPPs, and TSPPst (Christodes

[1]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[2]  Bodo Manthey,et al.  Approximation Algorithms for Multi-criteria Traveling Salesman Problems , 2006, WAOA.

[3]  Mihalis Yannakakis,et al.  The Traveling Salesman Problem with Distances One and Two , 1993, Math. Oper. Res..

[4]  Evripidis Bampis,et al.  Approximating the Pareto Curve with Local Search for the Bicriteria TSP (1, 2) Problem , 2003, FCT.

[5]  Evripidis Bampis,et al.  (Non)-Approximability for the Multi-criteria TSP(1, 2) , 2005, FCT.

[6]  A. J.,et al.  Analysis of Christofides ' heuristic : Some paths are more difficult than cycles , 2002 .

[7]  Bodo Manthey,et al.  On Approximating Multi-Criteria TSP , 2007, STACS.

[8]  M. Ehrgott.  Approximation algorithms for combinatorial multicriteria optimization problems , 2000 .

[9]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[10]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[11]  A. Warburton,et al.  Approximation Methods for Multiple Criteria Travelling Salesman Problems , 1987 .

[12]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[13]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems , 1998, JACM.

[14]  Santosh S. Vempala,et al.  On The Approximability Of The Traveling Salesman Problem , 2006, Comb..