Convergence of a Hill Climbing Genetic Algorithm for Graph Matching

This paper presents a convergence analysis for the problem of consistent labelling using genetic search. The work builds on a recent empirical study of graph matching where we showed that a Bayesian consistency measure could be efficiently optimised using a hybrid genetic search procedure which incorporated a hill-climbing step. In the present study we return to the algorithm and provide some theoretical justification for its observed convergence behaviour. The main conclusion of this study is that the hill-climbing step significantly accelerates convergence, and that the convergence rate is polynomial in the size of the node-set of the graphs being matched.