Deterministic Algorithms for Multi-criteria TSP

  • Bodo Manthey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6648)

Abstract

We present deterministic approximation algorithms for the multi-criteria traveling salesman problem (TSP). Our algorithms are faster and simpler than the existing randomized algorithms.

First, we devise algorithms for the symmetric and asymmetric multi-criteria Max-TSP that achieve ratios of 1/2k − ε and 1/(4k − 2) − ε, respectively, where k is the number of objective functions. For two objective functions, we obtain ratios of 3/8 − ε and 1/4 − ε for the symmetric and asymmetric TSP, respectively. Our algorithms are self-contained and do not use existing approximation schemes as black boxes.

Second, we adapt the generic cycle cover algorithm for Min-TSP. It achieves ratios of 3/2 + ε, \(\frac 12 + \frac{\gamma^3}{1-3\gamma^2} + \varepsilon\), and \(\frac 12 + \frac{\gamma^2}{1-\gamma} + \varepsilon\) for multi-criteria Min-ATSP with distances 1 and 2, Min-ATSP with γ-triangle inequality and Min-STSP with γ-triangle inequality, respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bodo Manthey
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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