The graph matching problem

• Published in: Pattern analysis and applications : PAA Vol. 16; no. 3; pp. 253 - 283
• Main Authors: Livi, Lorenzo, Rizzi, Antonello
• Format: Journal Article
• Language: English
• Published: London Springer London 01.08.2013; Springer
• Subjects: Applied sciences; Artificial intelligence; Computer Science; Computer science; control theory; systems; Exact sciences and technology; Information retrieval. Graph; Information systems. Data bases; Logical, boolean and switching functions; Memory organisation. Data processing; Pattern Recognition; Software; Survey; Theoretical computing; Graph kernels; Graph-based pattern recognition; Graph embedding; Inexact graph matching; Graph edit distance; Branching; Expert system; String matching; Search engine; Algorithmics; Embedding; Graph theory; Pattern recognition; Character string; Inductive logic programming; Inference rule; Distance; Graph matching
• ISSN: 1433-7541; 1433-755X
• DOI: 10.1007/s10044-012-0284-8

In this paper, we propose a survey concerning the state of the art of the graph matching problem , conceived as the most important element in the definition of inductive inference engines in graph-based pattern recognition applications. We review both methodological and algorithmic results, focusing on inexact graph matching procedures. We consider different classes of graphs that are roughly differentiated considering the complexity of the defined labels for both vertices and edges. Emphasis will be given to the understanding of the underlying methodological aspects of each identified research branch. A selection of inexact graph matching algorithms is proposed and synthetically described, aiming at explaining some significant instances of each graph matching methodology mainly considered in the technical literature.