Parametric alignment of ordered trees

Abstract

Motivation: Computing the similarity between two ordered trees has applications in RNA secondary structure comparison, genetics and chemical structure analysis. Alignment of tree is one of the proposed measures. Similar to pair-wise sequence comparison, there is often disagreement about how to weight matches, mismatches, indels and gaps when we compare two trees. For sequence comparison, the parametric sequence alignment tools have been developed. The users are allowed to see explicitly and completely the effect of parameter choices on the optimal sequence alignments. A similar tool for aligning two ordered trees is required in practice. Results: We develop a parametric tool for aligning two ordered trees that allow users to see the effect of parameter choices on the optimal alignment of trees. Our contributions include: (1) develop a parametric tool for aligning two ordered trees; (2) design an efficient algorithm for aligning two ordered trees with gap penalties that runs in O(n2deg2) time, where n is the number of nodes in the trees and deg is the degree of the trees; and (3) reduce the space of the algorithm from O(n2deg) to O(n log n · deg2).