Abstract
A new and efficient procedure for testing a pair of digraphs for isomorphism is developed. It is based on conducting a depth-first search on one of the digraphs followed by a systematic matching of edges using backtracking with very effective pruning. It is proved that for digraphs (ofn vertices) the expected time complexity of this procedure isO(n logn). This theoretical result is verified empirically on more than 300 large random digraphs. This procedure is shown to be more efficient than any of the existing general isomorphism procedures.
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References
A. V. Aho, J. E. Hopcroft and J. D. Ullman,The Design and Analysis of Computer Algorithms. Addison-Wesley. (1974).
A. T. Berztiss,A backtrack procedure for isomorphism of directed graphs, JACM 20, 3 (July 1973) 365–377.
K. S. Booth,Problems Polynomially Equivalent to Graph Isomorphism, Proc. of Symposium on Analytic Computational Complexity, Carnegie-Mellon University, (1976), 36.
D. G. Corneil,Graph Isomorphism, Ph.D. th., U. of Toronto, Toronto, Ontario, Canada, 1968.
D. G. Corneil and C. C. Gotlieb,An efficient algorithm for graph isomorphism, J.ACM 17, 1 (Jan. 1970), 51–64.
D. G. Corneil,The analysis of graph theoretic algorithms, Technical Report No. 65, Department of Computer Science, University of Toronto, Ontario, Canada (April 1974).
N. Deo,Graph Theory with Applications to Engineering and Computer Science. Prentice-Hall, Englewood Cliffs, N.J., 1974.
F. Harary,Graph Theory. Addison-Wesley, Reading, Mass., 1969.
F. Harary, C. A. King, A. Mowshowitz and R. C. Read,Cospectral graphs and digraphs, Bulletin Lond. Math. Soc., 3, (1971), 321–328.
J. E. Hopcroft and R. E. Tarjan,Isomorphism of planar graphs, Complexity of Computer Computations, Ed. R. E. Miller and J. W. Tatcher, Plenum (1972), 131–152.
J. E. Hopcroft and R. E. Tarjan,Efficient algorithms for graph manipulation — Algorithm 447, CACM 16, 6 (June 1973) 372–378.
R. M. Karp,Reducibility among combinatorial problems, In Complexity of Computer Computations, R. E. Miller and J. W. Tatcher, Eds. Plenum Press, New York, 1972, 85–103.
J. Lederberg,Topology of molecules, in The Mathematical Sciences, M.I.T. Press, Cambridge, Mass., 1969, 37–51.
G. Levi,Graph isomorphism: a heuristic edge-partitioning-oriented program, Computing, 12, (1974), 291–313.
A. Proskurowski,Search for a Unique Incidence Matrix of a Graph, BIT, 14 (1974), 209–226.
E. Sussenguth, Jr.,A graph theoretical algorithm for matching chemical structures, J. Chem. Doc. 5, 1 (February 1965) 36–43.
R. E. Tarjan,Depth-first search and linear graph algorithms, SIAM J. Comput. 1, 2 (1972) 146–160.
J. R. Ullman,An Algorithm for Subgraph Isomorphism, J. ACM, 23 (1976), 31–42.
S. H. Unger,GIT—A heuristic program for testing pairs of directed line graphs for isomorphism, Comm. ACM 7, 1 (Jan. 1964), 26–34.
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Deo, N., Davis, J.M. & Lord, R.E. A new algorithm for digraph isomorphism. BIT 17, 16–30 (1977). https://doi.org/10.1007/BF01932396
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DOI: https://doi.org/10.1007/BF01932396