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Efficiently indexing shortest paths by exploiting symmetry in graphs

Yanghua Xiao,Wentao Wu,J. Pei,Wei Wang,Zhenying He

Published 2009 in International Conference on Extending Database Technology

ABSTRACT

Shortest path queries (SPQ) are essential in many graph analysis and mining tasks. However, answering shortest path queries on-the-fly on large graphs is costly. To online answer shortest path queries, we may materialize and index shortest paths. However, a straightforward index of all shortest paths in a graph of N vertices takes O(N2) space. In this paper, we tackle the problem of indexing shortest paths and online answering shortest path queries. As many large real graphs are shown richly symmetric, the central idea of our approach is to use graph symmetry to reduce the index size while retaining the correctness and the efficiency of shortest path query answering. Technically, we develop a framework to index a large graph at the orbit level instead of the vertex level so that the number of breadth-first search trees materialized is reduced from O(N) to O(|Δ|), where |Δ| ≤ N is the number of orbits in the graph. We explore orbit adjacency and local symmetry to obtain compact breadth-first-search trees (compact BFS-trees). An extensive empirical study using both synthetic data and real data shows that compact BFS-trees can be built efficiently and the space cost can be reduced substantially. Moreover, online shortest path query answering can be achieved using compact BFS-trees.

PUBLICATION RECORD

  • Publication year

    2009

  • Venue

    International Conference on Extending Database Technology

  • Publication date

    2009-03-24

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    DOI 10.1145/1516360.1516418
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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