Segmental Distance between Rooted Labeled Caterpillars

Abstract

A segmental distance for rooted labeled unordered trees is the edit distance such that the insertion and the deletion in the edit operations are allowed to either the root or the leaves. In this paper, we design the algorithm of computing the segmental distance for rooted labeled caterpillars in O(n+h2σ) time under the unit cost function, where n is the maximum number of vertices, h is the maximum height and σ is the number of labels, whereas the problem of computing the segmental distance for rooted labeled unordered trees is MAX SNP-hard.