Efficient algorithms on trees and graphs with unique node labels

Abstract

There is a growing interest on trees and graphs with unique node labels in the field of pattern recognition, not only because graph isomorphism and related problems become polynomial-time solvable when restricted to them but also in the light of important practical applications in structural pattern recognition. Current algorithms for testing graph and subgraph isomorphism and computing the graph edit distance, a shortest edit script, a largest common subgraph, and a smallest common supergraph of two graphs with unique node labels, take time quadratic in the number of nodes in the graphs, and the same holds for similar problems on trees with unique node labels. In this paper, simple algorithms are presented for solving these problems in time linear in the number of nodes and edges in the trees or graphs. These new algorithms are based on radix sorting the sets of nodes and edges in the trees or graphs by node label and source and target node label, respectively, followed by a simultaneous traversal of the ordered sets of nodes and edges. © Springer-Verlag Berlin Heidelberg 2007.