A Hard Dial-a-Ride Problem that is Easy on Average

Authors:
Amin Coja-Oghlan;Sven O. Krumke;Till Nierhoff
Affiliations:
Institut für Informatik Unter den Linden 6, Humboldt-Universität zu Berlin, Berlin, Germany 10099;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany 67653;Institut für Informatik Unter den Linden 6, Humboldt-Universität zu Berlin, Berlin, Germany 10099
Venue:
Journal of Scheduling
Year:
2005

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Abstract

In the dial-a-ride-problem (Darp) objects have to be moved between given sources and destinations in a transportation network by means of a server. The goal is to find the shortest transportation for the server. We study the Darp when the underlying transportation network forms a caterpillar. This special case is strongly NP-hard in the worst case. We prove that in a probabilistic setting there exists a polynomial time algorithm that finds an optimal solution with high probability. Moreover, with high probability the optimality of the solution found can be certified efficiently. In addition, we examine the complexity of the Darp in a semirandom setting and in the unweighted case.