Finding similar consensus between trees: An algorithm and a distance hierarchy

The problem of finding this similar consensus (also known as the largest approximately common substructures) of two trees arises in many pattern recognition applications. This paper presents a dynamic programming algorithm to solve the problem based on the distance measure originated from Tanaka and Tanaka. The algorithm runs as fast as the best-known algorithm for comparing two trees using Tanaka's distance measure when the allowed distance between the common substructures is a constant independent of the input trees. In addition, we establish a hierarchy among Tanaka's distance measure and three other edit-based distance measures published in the literature.