Reoptimization of minimum and maximum traveling salesman's tours

Authors:
Giorgio Ausiello;Bruno Escoffier;JéRôMe Monnot;Vangelis Paschos
Affiliations:
Dipartimento di Informatica e Sistemistica, Universití di Roma "La Sapienza", Roma, Italy;Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France and CNRS, UMR 7024, F-75775 Paris, France;Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France and CNRS, UMR 7024, F-75775 Paris, France;Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France and CNRS, UMR 7024, F-75775 Paris, France
Venue:
Journal of Discrete Algorithms
Year:
2009

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Abstract

In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5-approximation algorithm for the reoptimization version of MaxTSP.