Multi-Criteria TSP: Min and Max Combined

  • Bodo Manthey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5893)

Abstract

We present randomized approximation algorithms for multi-criteria traveling salesman problems (TSP), where some objective functions should be minimized while others should be maximized. For the symmetric multi-criteria TSP (STSP), we present an algorithm that computes (2/3 − ε, 4 + ε) approximate Pareto curves. Here, the first parameter is the approximation ratio for the objectives that should be maximized, and the second parameter is the ratio for the objectives that should be minimized. For the asymmetric multi-criteria TSP (ATSP), we present an algorithm that computes (1/2 − ε, log2n + ε) approximate Pareto curves. In order to obtain these results, we simplify the existing approximation algorithms for multi-criteria Max-STSP and Max-ATSP. Finally, we give algorithms with improved ratios for some special cases.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bodo Manthey
    • 1
  1. 1.University of TwenteDepartment of Applied MathematicsAE EnschedeThe Netherlands

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