Approximation Algorithms for Min-Max Path Cover Problems with Service Handling Time

Authors:
Zhou Xu;Liang Xu
Affiliations:
Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hong Kong;Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hong Kong
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

This paper presents improved approximation algorithms and inapproximability results for min-max path cover problems with service handling time, which have wide applications in practice when the latest service completion time for customers is critical. We study three variants of this problem, where paths must start (i) from a given depot, (ii) from any depot of a given set, and (iii) from any vertex of the given graph, respectively. For these three variants, we are able to achieve approximation ratios of 3, (4 + 驴), and (5 + 驴), respectively, for any 驴 0. We have further shown that approximation ratios less than 4/3, 3/2, and 3/2 are impossible for them, respectively, unless NP = P.