Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6875548 | Theoretical Computer Science | 2018 | 15 Pages |
Abstract
UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a widely used clustering method. Here we show that UPGMA is a greedy heuristic for the normalized equidistant minimum evolution (NEME) problem, that is, finding a rooted tree that minimizes the minimum evolution score relative to the dissimilarity matrix among all rooted trees with the same leaf-set in which all leaves have the same distance to the root. We prove that the NEME problem is NP-hard. In addition, we present some heuristic and approximation algorithms for solving the NEME problem, including a polynomial time algorithm that yields a binary, rooted tree whose NEME score is within O(log2â¡n) of the optimum.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Vincent Moulton, Andreas Spillner, Taoyang Wu,