Partitioning graphs to speed up dijkstra's algorithm

  • Authors:

  • Rolf H. Möhring;Heiko Schilling;Birk Schütz;Dorothea Wagner;Thomas Willhalm

  • Affiliations:

  • Institut für Mathematik, Technische Universität Berlin, Berlin, Germany;Institut für Mathematik, Technische Universität Berlin, Berlin, Germany;Fakultät für Informatik, Universität Karlsruhe, Karlsruhe, Germany;Fakultät für Informatik, Universität Karlsruhe, Karlsruhe, Germany;Fakultät für Informatik, Universität Karlsruhe, Karlsruhe, Germany

  • Venue:
  • WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
  • Year:
  • 2005

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Abstract

In this paper, we consider Dijkstra's algorithm for the point-to-point shortest path problem in large and sparse graphs with a given layout. In [1], a method has been presented that uses a partitioning of the graph to perform a preprocessing which allows to speed-up Dijkstra's algorithm considerably. We present an experimental study that evaluates which partitioning methods are suited for this approach. In particular, we examine partitioning algorithms from computational geometry and compare their impact on the speed-up of the shortest-path algorithm. Using a suited partitioning algorithm speed-up factors of 500 and more were achieved. Furthermore, we present an extension of this speed-up technique to multiple levels of partitionings. With this multi-level variant, the same speed-up factors can be achieved with smaller space requirements. It can therefore be seen as a compression of the precomputed data that conserves the correctness of the computed shortest paths.