article

Partitioning graphs to speedup Dijkstra's algorithm

Authors:

Rolf H. Möhring,

Heiko Schilling,

Dorothea Wagner,

Thomas WillhalmAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 11

Pages 2.8 - es

https://doi.org/10.1145/1187436.1216585

Published: 09 February 2007 Publication History

Abstract

We study an acceleration method for point-to-point shortest-path computations in large and sparse directed graphs with given nonnegative arc weights. The acceleration method is called the arc-flag approach and is based on Dijkstra's algorithm. In the arc-flag approach, we allow a preprocessing of the network data to generate additional information, which is then used to speedup shortest-path queries. In the preprocessing phase, the graph is divided into regions and information is gathered on whether an arc is on a shortest path into a given region. The arc-flag method combined with an appropriate partitioning and a bidirected search achieves an average speedup factor of more than 500 compared to the standard algorithm of Dijkstra on large networks (1 million nodes, 2.5 million arcs). This combination narrows down the search space of Dijkstra's algorithm to almost the size of the corresponding shortest path for long-distance shortest-path queries. We conduct an experimental study that evaluates which partitionings are best suited for the arc-flag method. In particular, we examine partitioning algorithms from computational geometry and a multiway arc separator partitioning. The evaluation was done on German road networks. The impact of different partitions on the speedup of the shortest path algorithm are compared. Furthermore, we present an extension of the speedup technique to multiple levels of partitions. With this multilevel variant, the same speedup factors can be achieved with smaller space requirements. It can, therefore, be seen as a compression of the precomputed data that preserves the correctness of the computed shortest paths.

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Index Terms

Partitioning graphs to speedup Dijkstra's algorithm
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 11, Issue

2006

355 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/1187436

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Copyright © 2007 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 February 2007

Published in JEA Volume 11

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