Specification of error distances for graphs by precedence graph grammars and fast recognition of similarity

Abstract

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(n3) time, n the number of nodes of the whole input graph. Futhermore the parse tree of the most similar graph is computed, thus providing further processing steps with an efficient hierarchical decomposition.CR Categories and Subject DescriptorsI.5.1 [Pattern Recognition]: Models-statistical, structural F.4.2 [Mathematical Logic and Formal Languages]: Grammars and Other Rewriting Systems-parsing G.2.2 [Discrete Mathematics]: Graph Theory- graph algorithms, trees Additional Key Words and Phrasesinexact graph matchingsimilarity of graphserror distance between graphsgraph grammargraph parserprecedence relationsparallel parsinghierarchical graph model