# Approximation algorithms for multi-criteria traveling salesman problems

Manthey, B.
and
Shankar Ram, L.
(2009)
*Approximation algorithms for multi-criteria traveling salesman problems.*
Algorithmica, 53
(1).
pp. 69-88.
ISSN 0178-4617

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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 -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 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 -triangle inequality ratio ), asymmetric TSP (ATSP) with -triangle inequality (ratio ), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2). |

Item Type: | Article |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/68059 |

Official URL: | http://dx.doi.org/10.1007/s00453-007-9011-z |

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