An Algorithm for Subgraph Isomorphism

TLDR

Subgraph isomorphism is traditionally solved by brute‑force tree‑search enumeration. The paper introduces a new algorithm that improves efficiency by inferentially eliminating successor nodes during tree search. The algorithm uses tree‑search with inferential pruning, tested on subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism with random and nonrandom graphs, and includes a parallel asynchronous logic‑in‑memory component for future hardware. Experiments show the algorithm reduces runtime, and the proposed hardware would enable very rapid isomorphism determination.

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 algorithm, subgraph isomorphism, clique 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 built. The hardware implementation would allow very rapid determination of isomorphism.