An algorithm using length-r paths to approximate subgraph isomorphism

The 'LeRP' algorithm approximates subgraph isomorphism for attributed graphs based on counts of length-r paths. The algorithm provides a good approximation to the maximal isomorphic subgraph. The basic approach of the LeRP algorithm differs fundamentally from other methods. When comparing structural similarity LeRP uses a neighborhood of nodes that varies in size dynamically. This approach provides sufficient evidence of similarity to permit LeRP to form a node-to-node mapping and can be computed with polynomial effort in the worst-case. Results from over 32,000 simulated cases are reported. We demonstrate that LeRP does not need a high dynamic range of node and edge coloring to perform well. For example, LeRP can input 50-node and 100-node graphs that contain a common 50-node subgraph, and then compute a matching subgraph having 49.74 +/- 0.46 nodes (mean one standard deviation). This takes from 0.4 to 0.5 s. In this example, 100 trials were evaluated and graphs had discrete coloring for nodes and edges with a dynamic range of four. Test conditions are varied and include strongly regular graphs as well as Model A. (C) 2002 Published by Elsevier Science B.V.