Simple and efficient graph compression schemes for dense and complement graphs

  • Ming-Yang Kao
  • Shang-Hua Teng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)


In this paper, we present two graph compression schemes for solving problems on dense graphs and complement graphs. They compress a graph or its complement graph into two kinds of succinct representations based on adjacency intervals and adjacency integers, respectively. These two schemes complement each other for different ranges of density. Using these schemes, we develop optimal or near optimal algorithms for fundamental graph problems. In contrast to previous graph compression schemes, ours are simple and efficient for practical applications.


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  1. [1]
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.Google Scholar
  2. [2]
    V. L. Arlazarov, E. A. Dinic, M. A. Kronrod, and I. A. Faradzev. On economical construction of the transitive closure of a directed graph. Dokl. Akad. Nauk SSSR, 194:487–488, 1970.Google Scholar
  3. [3]
    J. Cheriyan, M. Y. Kao, and R. Thurimella. Scan-first search and sparse certificates: An improved parallel algorithm for k-vertex connectivity. SIAM Journal on Computing, 22(1):157–174, 1993.Google Scholar
  4. [4]
    T. H. Cormen, C. L. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1991.Google Scholar
  5. [5]
    T. Feder and R. Motwani. Clique partitions, graph compression, and speeding-up algorithms. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 123–133, 1991.Google Scholar
  6. [6]
    M. L. Fredman and M. E. Saks. The cell probe complexity of dynamic data structures. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 345–354, 1989.Google Scholar
  7. [7]
    H. N. Gabow and R. E. Tarjan. A linear-time algorithm for a special case of disjoint set union. Journal of Computer and System Sciences, 30(2):209–221, 1985.Google Scholar
  8. [8]
    R. E. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the ACM, 22(2):215–225, 1975.Google Scholar
  9. [9]
    R. E. Tarjan. A class of algorithms which require nonlinear time to maintain disjoint sets. Journal of Computer and System Sciences, 18(2):110–127, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ming-Yang Kao
    • 1
  • Shang-Hua Teng
    • 2
  1. 1.Department of Computer ScienceDuke UniversityDurham
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridge

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