Algorithms for approximate graph matching

Labeled graphs are graphs in which each node and edge has a label. The distance between two labeled graphs is considered to be the weighted sum of the costs of edit operations (insert, delete, and relabel the nodes and edges) to transform one graph to the other. The paper considers two variants of the approximate graph matching problem (AGM): Given a pattern graph P and a data graph D: 1. 1. What is the distance between P and D? 2. 2. What is the minimum distance between P and D when subgraphs can be freely removed from D? We first show that no efficient algorithm can solve either variant of the AGM unless P = NP. Then we present several heuristic algorithms leading to approximate solutions. The heuristics are based on probabilistic hill climbing and maximum flow techniques. Our experimental results involving the comparison of real and simulated data demonstrate the good performance of the algorithms presented.