Linear computation of the maximum simultaneous forward and backward bisimulation for node-labeled trees

Abstract

The F&B-index is used to speed up pattern matching in tree and graph data, and is based on the maximum F&B-bisimulation, which can be computed in loglinear time for graphs. It has been shown that the maximum F-bisimulation can be computed in linear time for DAGs. We build on this result, and introduce a linear algorithm for computing the maximum F&B-bisimulation for tree data. It first computes the maximum F-bisimulation, and then refines this to a maximal B-bisimulation. We prove that the result equals the maximum F&B-bisimulation. © 2010 Springer-Verlag.