Anchored Alignment Problem for Rooted Labeled Trees

Abstract

An anchored alignment tree between two rooted labeled trees with respect to a mapping that is a correspondence between nodes in two trees, called an anchoring, is an alignment tree which contains a node labeled by a pair of labels for every pair of nodes in the anchoring. In this paper, we formulate an anchored alignment problem as the problem, when two rooted labeled trees and an anchoring between them are given as input, to output an anchored alignment tree if there exists; to return “no” otherwise. Then, we show that the anchored alignment problem can be solved in $O(h\alpha ^2+n+m)$ time and in $O(h\alpha )$ space, where n is the number of nodes in a tree, m is the number of nodes in another tree, h is the maximum height of two trees and $\alpha$ is the cardinality of an anchoring.

This work is partially supported by Grant-in-Aid for Scientific Research 24240021, 24300060, 25540137, 26280085 and 26370281 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.