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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.

Keywords

Approximation Algorithm Approximation Ratio Edge Weight Travel Salesman Problem Travel Salesman Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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