Semi-preemptive routing on trees

Authors:
Sven O. Krumke;Dirk Räbiger;Rainer Schrader
Affiliations:
Department of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 14, 67653 Kaiserslautern, Germany;Zentrum für Angewandte Informatik, Universität zu Köln, Weyertal 80, 50931 Köln, Germany;Zentrum für Angewandte Informatik, Universität zu Köln, Weyertal 80, 50931 Köln, Germany
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We study a variant of the pickup-and-delivery problem (PDP) in which the objects that have to be transported can be reloaded at most d times, for a given d@?N. This problem is known to be polynomially solvable on paths or cycles and NP-complete on trees. We present a (4/3+@e)-approximation algorithm if the underlying graph is a tree. By using a result of Charikar et al. [M. Charikar, C. Chekuri, A. Goel, S. Guha, S. Plotkin, Approximating a finite metric by a small number of tree metrics, in: FOCS '98: Proceedings of the 39th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, USA, 1998, pp. 379-388], this can be extended to a O(lognloglogn)-approximation for general graphs.