A Theoretical Analysis of Alignment and Edit Problems for Trees

Abstract

The problem of comparing two tree structures emerges across a wide range of applications in computational biology, pattern recognition, and many others. A number of tree edit methods have been proposed to find a structural similarity between trees. The alignment of trees is one of these methods, introduced as a natural extension of the alignment of strings, which gives a common supertree pattern of two trees, whereas tree edit gives a common subtree pattern. It is well known that alignment and edit are two equivalent notions for strings from the computational point of view. This equivalence, however, does not hold for trees. The lack of a theoretical formulation of these notions has lead to confusion. In this paper, we give a theoretical analysis of alignment and edit methods, and show an important relationship, which is the equivalence between the the alignment of trees and a variant of tree edit, called less-constrained edit.

This work is partly supported by Grant-in-Aid for Scientific Research No. 17700138, and No. 16016275 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.