Optimal Algorithm for Finding Representation of Subtree Distance

Abstract

In this paper, we address the problem of finding a representation of a subtree distance, which is an extension of a tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give an O(n²) time algorithm that finds such a representation, where n is the size of the ground set. Since a lower bound of the problem is Ω(n²), our algorithm achieves the optimal time complexity.