Computing the Minimum Error Distance of Graphs in 0(n³) Time with Precedence Graph Grammars

Summary

A major part in structural pattern recognition is inexact graph matching. Typically some node and edge labelled graph has to be matched against a possibly infinite graph language, which represents the set of all correct patterns. The task is to identify that correct pattern, that is most similar to the input graph. Similarity is defined by weighted editing operations, yielding an error distance. Computing the minimum error distance even for two graphs only is NP-complete. In order to gain efficient procedures application dependent knowledge has to be involved. In this paper a graph parser generator is presented, that can be adapted to a wide range of applications easily. A precedence graph grammar is used to describe the structural knowledge about the class of all correct patterns. The weights for editing operations on graphs provide the statistical knowledge. By restricting, backtracking to subgraphs of constant size, the minimum error distance is computed in O(ir) time, n the number of nodes of the whole input graph. Furthermore the parse tree of the most similar graph is computed, thus providing further processing steps with an efficient hierarchical decomposition.