External-memory graph algorithms

Yi Jen Chiang, Michael T. Goodrich, Edward F. Grove, Roberto Tamassia, Darren Erik Vengroff, Jeffrey Scott Vitter

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: • Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we call the "proximate neighbors" problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. • PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms. • Time-forward processing. We present a general technique for evaluating circuits (or "circuit-like" computations) in external memory. We also use this in a deterministic list ranking algorithm. • Deterministic 3-coloring of a cycle. We give several optimal methods for 3-coloring a cycle, which can be used as a subroutine for finding large independent sets for list ranking. Our ideas go beyond a straightforward PRAM simulation, and may be of independent interest. • External depth-first search. We discuss a method for performing depth first search and solving related problems efficiently in external memory. Our technique can be used in conjunction with ideas due to Ullman and Yannakakis in order to solve graph problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold. Our techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
    PublisherAssociation for Computing Machinery
    Pages139-149
    Number of pages11
    ISBN (Electronic)0898713498
    StatePublished - Jan 22 1995
    Event6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States
    Duration: Jan 22 1995Jan 24 1995

    Publication series

    NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

    Other

    Other6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
    CountryUnited States
    CitySan Francisco
    Period1/22/951/24/95

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    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Cite this

    Chiang, Y. J., Goodrich, M. T., Grove, E. F., Tamassia, R., Vengroff, D. E., & Vitter, J. S. (1995). External-memory graph algorithms. In Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 (pp. 139-149). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery.