On the Informational Asymmetry between Upper and Lower Bounds for Ultrametric Evolutionary Trees

Abstract. This paper addresses the informational asymmetry for constructing an ultrametric evolutionary tree from upper and lower bounds on pairwise distances between n given species. We show that the tallest ultrametric tree exists and can be constructed in O(n2 ) time, while the existence of the shortest ultrametric tree depends on whether the lower bounds are ultrametric. The tallest tree construction algorithm gives a very simple solution to the construction of an ultrametric tree. We also provide an e cient O(n2 )-time algorithm for checking the uniqueness of an ultrametric tree, and study a query problem for testing whether an ultrametric tree satis es both upper and lower bounds.

• Type: Conference
• Year: 1999
• Where: ESA
• Authors: Ting Chen, Ming-Yang Kao
• Keywords: Algorithms, ESA 1999, Lower Bounds, Tallest Ultrametric Tree, Ultrametric Tree