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

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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.

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Authors and Affiliations

  1. Institut für Informatik Unter den Linden 6, Humboldt-Universität zu Berlin, 10099, Berlin, Germany

    Amin Coja-Oghlan & Till Nierhoff

  2. Department of Mathematics, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Sven O. Krumke

Authors
  1. Amin Coja-Oghlan
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  2. Sven O. Krumke
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  3. Till Nierhoff
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Corresponding author

Correspondence to Sven O. Krumke.

Additional information

Research supported by the German Science Foundation (DFG, grant FOR 413/1-1)

Research supported by the German Science Foundation (DFG, grant Gr 883/10)

Research supported by the German Science Foundation (DFG, grant PR 296/6-3)

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Coja-Oghlan, A., Krumke, S.O. & Nierhoff, T. A Hard Dial-a-Ride Problem that is Easy on Average. J Sched 8, 197–210 (2005). https://doi.org/10.1007/s10951-005-6811-3

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  • DOI: https://doi.org/10.1007/s10951-005-6811-3

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