Sibling distance for rooted labeled trees

Abstract

In this paper, we introduce a sibling distance ds for rooted labeled trees as an L1-distance between their sibling histograms, which consist of the frequencies of every pair of the label of a node and the sequence of labels of its children. Then, we show that δs gives a constant factor lower bound on the tree edit distance δ such that δ s(T1, T2) ≤ 4δ(T1, T2). Next, we design the algorithm to compute the sibling histogram in O(n) time for ordered trees and in O(gn) time for unordered trees, where n and g are the number of nodes and the degree of a tree. Finally, we give experimental results by applying the sibling distance to glycan data. © Springer-Verlag Berlin Heidelberg 2009.