A Fast Backtracking Algorithm to Test Directed Graphs for Isomorphism Using Distance Matrices

  • Authors:
  • Douglas C. Schmidt;Larry E. Druffel

  • Affiliations:
  • Systems and Information Science Department, Vanderbilt University, Box 6146, Station B, Nashville, TN;Department of Astronautics and Computer Science, United States Air Force Academy, CO

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1976

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Abstract

A backtracking algorithm for testing a pair of digraphs for isomorphism is presented. The information contained in the distance matrix representation of a graph is used to establish an initial partition of the graph's vertices. This distance matrix information is then applied in a backtracking procedure to reduce the search tree of possible mappings. While the algorithm is not guaranteed to run in polynomial time, it performs efficiently for a large class of graphs.