A heuristic for the Stacker Crane Problem on trees which is almost surely exact

  • Authors:

  • Amin Coja-Oghlan;Sven O. Krumke;Till Nierhoff

  • Affiliations:

  • Humboldt-Universität zu Berlin, Institut für Informatik, Unter den Linden 6, 10099 Berlin, Germany;Konrad-Zuse-Zentrum für Informationstechnik Berlin, Department Optimization, Takustr. 7, 14195 Berlin-Dahlem, Germany;International Computer Science Institute, 1947 Center St., Berkeley, CA 94704, USA

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2006

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Abstract

Given an edge-weighted transportation network G and a list of transportation requests L, the Stacker Crane Problem is to find a minimum-cost tour for a server along the edges of G that serves all requests. The server has capacity one, and starts and stops at the same vertex. In this paper, we consider the case that the transportation network G is a tree, and that the requests are chosen randomly according to a certain class of probability distributions. We show that a polynomial time algorithm by Frederickson and Guan [J. Algorithms 15 (1993) 29-60], which guarantees a 4/3-approximation in the worst case, on almost all inputs finds a minimum-cost tour, along with a certificate of the optimality of its output.