Alignment of Cyclically Ordered Trees

Abstract

In this paper, we investigate an alignment distance between the following three cyclically ordered trees. A biordered tree is an unordered tree that allows both a left-to-right and a right-to-left order among siblings. A cyclic-ordered tree is an unordered tree that allows cyclic order among siblings in a left-to-right direction. A cyclic-biordered tree is an unordered tree that allows cyclic order among siblings in both left-to-right and right-to-left directions. Then, we design the algorithms to compute the distance between biordered trees in O(n2D2) time and ones between cyclic-ordered trees and cyclic-biordered trees in O(n2D4) time, where n is the maximum number of nodes and D is the maximum degree in two given trees.