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16978 On approximating multi-criteria TSP

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Manthey, B. (2009) On approximating multi-criteria TSP. In: Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, 26-28 Feb 2009, Freiburg, Germany. pp. 637-648. Dagstuhl Research Online Publication Server. ISBN 978-3-939897-09-5

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Official URL: http://drops.dagstuhl.de/opus/volltexte/2009/1853/

Abstract

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For multi-criteria Max-STSP, where the edge weights have to be symmetric, we devise an algorithm that achieves an approximation ratio of $2/3 - \varepsilon$ . For multi-criteria Max-ATSP, where the edge weights may be asymmetric, we present an algorithm with an approximation ratio of $1/2 - \varepsilon$ . Our algorithms work for any fixed number $k$ of objectives. To get these ratios, we introduce a decomposition technique for cycle covers. These decompositions are optimal in the sense that no decomposition can always yield more than a fraction of $2/3$ and $1/2$ , respectively, of the weight of a cycle cover. Furthermore, we present a deterministic algorithm for bi-criteria Max-STSP $\$ that achieves an approximation ratio of $61/243 \approx 1/4$ . Finally, we present a randomized approximation algorithm for the asymmetric multi-criteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of $\log n + \varepsilon$ . For this variant of multi-criteria TSP, this is the first approximation algorithm we are aware of. If the distances fulfil the $\gamma$ -triangle inequality, its ratio is $1/(1-\gamma) + \varepsilon$ .

Item Type:	Conference or Workshop Paper (Full Paper, Talk)
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
Uncontrolled Keywords:	Traveling salesman problem, TSP, Approximation algorithms, Multi-criteria optimization, Multi-objective optimization
ID Code:	16978
Status:	Published
Deposited On:	10 December 2009
Refereed:	Yes
International:	Yes
More Information:	statistics metis

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