ABSTRACT. Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algomthm, subgraph isomorphism, chque detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs.A parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is also described, although this hardware has not actually been bmlt The hardware implementation would allow very rapid determination of isomorphism.

Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Analytical prediction of quantitative performance of partition search appears to be intractable and evaluation therefore has to be by experimental comparison with reduction search algorithms that represent the state of the art. Instead of working only with available reduction search algorithms, this paper introduces enhancements such as semijoin reduction preprocessing using Bloom filtering.

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A solution to a binary constraint satisfaction problem is a set of discrete values, one in each of a given set of domains, subject to constraints that allow only prescribed pairs of values in specified pairs of domains. Solutions are sought by backtrack search interleaved with a process that removes from domains those values that are currently inconsistent with provisional choices already made in the course of search. For each value in a given domain, a bit-vector shows which values in another domain are or are not permitted in a solution. Bit-vector representation of constraints allows bit-parallel, therefore fast, operations for editing domains during search. This article revises and updates bit-vector algorithms published in the 1970's, and introduces focus search, which is a new bit-vector algorithm relying more on search and less on domain-editing than previous algorithms. Focus search is competitive within a limited family of constraint satisfaction problems.Determination of subgraph isomorphism is a specialized binary constraint satisfaction problem for which bit-vector algorithms have been widely used since the 1980's, particularly for matching molecular structures. This article very substantially updates the author's 1976 subgraph isomorphism algorithm, and reports experimental results with random and real-life data.

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