Abstract
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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A.V. Aho, J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley: Reading, MA, 1974.
A.V. Aho, J.E. Hopcroft, and J.D. Ullman, Data Structures and Algorithms, Addison-Wesley: Reading, MA, 1983.
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, vol. 194, pp. 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, vol. 22, no.1, pp. 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, 1991, pp. 123–133.
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, 1989, pp. 345–354.
H.N. Gabowand R.E. Tarjan, “A linear-time algorithm for a special case of disjoint set union,” Journal of Computer and System Sciences, vol. 30, no.2, pp. 209–221, 1985.
D. Gusfield, “A graph theoretic approach to statistical data security,” SIAM Journal on Computing, vol. 17, pp. 552–571, 1988.
E. Horowitz and S. Sahni, Fundamentals of Data Structures, Computer Science Press: New York, 1976.
M.Y. Kao, “Data security equals graph connectivity,” SIAM Journal on Discrete Mathematics, vol. 9, pp. 87–100, 1996.
M.Y. Kao, “Efficient detection and protection of information in cross tabulated tables II: Minimal linear invariants,” Journal of Combinatorial Optimization, vol. 1, pp. 187–202, 1997a.
M.Y. Kao, “Total protection of analytic-invariant information in cross-tabulated tables,” SIAM Journal on Computing, vol. 26, no.1, pp. 231–242, 1997b.
M.Y. Kao and D. Gusfield, “Efficient detection and protection of information in cross tabulated tables I: Linear invariant test,” SIAM Journal on Discrete Mathematics, vol. 6, pp. 460–476, 1993.
R. Sedgewick, Algorithms, Addison-Wesley: Reading, MA, 1988.
R.E. Tarjan, “Depth-first search and linear graph algorithms,” SIAM Journal on Computing, vol. 1, pp. 146–160, 1972.
R.E. Tarjan, “Efficiency of a good but not linear set union algorithm,” Journal of the ACM, vol. 22, no.2, pp. 215–225, 1975.
R.E. Tarjan, “A class of algorithms which require nonlinear time to maintain disjoint sets,” Journal of Computer and System Sciences, vol. 18, no.2, pp. 110–127, 1979.
R.E. Tarjan, Data Structures and Network Algorithms, Society for Industrial and Applied Mathematics, 1983.
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Kao, MY., Occhiogrosso, N. & Teng, SH. Simple and Efficient Graph Compression Schemes for Dense and Complement Graphs. Journal of Combinatorial Optimization 2, 351–359 (1998). https://doi.org/10.1023/A:1009720402326
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DOI: https://doi.org/10.1023/A:1009720402326