Tree Isomorphism Algorithms: Speed vs. Clarity

Abstract

No algorithm, other than brute force, is known for testing whether two arbitrary graphs are isomorphic. In fact it is still an open question [3] whether graph isomorphism is NP complete. But polynomial time isomorphism algorithms for various graph subclasses such as trees are known (see [3, p. 285 and p. 339] for a summary). In gene splicing, protein analysis, and molecular biology the chemical structures are often trees with millions of vertices. In such applications, the difference between 0(n), 0(n log n), and O(n2) isomorphism algorithms is of practical not just theoretical importance. Readers of MATHEMATICS MAGAZINE will find it of interest to see how such algorithms evolve and are analyzed. As in an earlier article [2], we have chosen dialogue to capture the spirit of discovery and failure in the search for a fast and clear tree isomorphism algorithm.