Abstract
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.
Supported in part by NSF Grant CCR-9101385.
Supported in part by AFOSR F49620-92-J-0125 and Darpa N00014-92-J-1799.
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References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.
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.
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.
T. H. Cormen, C. L. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1991.
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.
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.
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.
R. E. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the ACM, 22(2):215–225, 1975.
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.
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© 1994 Springer-Verlag Berlin Heidelberg
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Kao, MY., Teng, SH. (1994). Simple and efficient graph compression schemes for dense and complement graphs. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_211
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DOI: https://doi.org/10.1007/3-540-58325-4_211
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Online ISBN: 978-3-540-48653-4
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