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An algorithm for tree-realizability of distance matrices

An algorithm for testing tree realizability of distance matrices is given. It is well-known that if a matrix D has a realization by a tree then such a realization is optimal and unique up to homeomorphism. Our algorithm produces a tree realization or a message that there is no such realization in time O(n 2) where n is the number of points in a finite metric space with the distance matrix D. An O(n 2) algorithm for computing distance matrix for a given tree is also given.