Optimally fast shortest path algorithms for some classes of graphs

Etsuro Moriya, Keiko Tsugane

    Research output: Contribution to journalArticle

    Abstract

    Two algorithms for shortest path problems are presented. One is to find the all-pairs shortest paths (APSP) that runs in O(n2Iogn + nm) time for n-vertex m-edge directed graphs consisting of strongly connected components with O(Iogn) edges among them. The other is to find the single-source shortest paths (SSSP) that runs in O(n) time for graphs reducible to the trivial graph by some simple transformations. These algorithms are optimally fast for some special classes of graphs in the sense that the former achieves O(n2) which is a lower bound of the time necessary to find APSP, and that the latter achieves O(n) which is a lower bound of the time necessary to find SSSP. The latter can be used to find APSP, also achieving the running time O(n2).

    Original languageEnglish
    Pages (from-to)297-317
    Number of pages21
    JournalInternational Journal of Computer Mathematics
    Volume70
    Issue number2
    Publication statusPublished - 1998

    Keywords

    • All-pairs shortest paths
    • Dijkstra's algorithm
    • Johnson's algorithm
    • Shortest path problem
    • Single-source shortest paths

    ASJC Scopus subject areas

    • Applied Mathematics

    Fingerprint Dive into the research topics of 'Optimally fast shortest path algorithms for some classes of graphs'. Together they form a unique fingerprint.

  • Cite this