Approximation Algorithms for Conflict-Free Vehicle Routing

  • Kaspar Schüpbach
  • Rico Zenklusen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


We consider a natural basic model for conflict-free routing of a group of k vehicles, a problem frequently encountered in many applications in transportation and logistics. There is a large gap between currently employed routing schemes and the theoretical understanding of the problem. Previous approaches have either essentially no theoretical guarantees, or suffer from high running times, severely limiting their usability. So far, no efficient algorithm is known with a sub-linear (in k) approximation guarantee and without restrictions on the graph topology.

We show that the conflict-free vehicle routing problem is hard to solve to optimality, even on paths. Building on a sequential routing scheme, we present an algorithm for trees with makespan bounded by O(OPT) + k. Combining this result with ideas known from packet routing, we obtain a first efficient algorithm with sub-linear approximation guarantee, namely an \(O(\sqrt{k})\)-approximation. Additionally, a randomized algorithm leading to a makespan of O(polylog(k))·OPT + k is presented that relies on tree embedding techniques applied to a compacted version of the graph to obtain an approximation guarantee independent of the graph size.


Approximation Algorithm Span Tree Vehicle Route Problem Graph Topology Container Terminal 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kaspar Schüpbach
    • 1
  • Rico Zenklusen
    • 2
  1. 1.Institute For Operations ResearchETH ZürichZürichSwitzerland
  2. 2.Department of MathematicsMITCambridgeUSA

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