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(log2n) of the optimum.
|Number of pages||15|
|Journal||Theoretical Computer Science|
|Early online date||1 Feb 2018|
|Publication status||Published - 18 Apr 2018|
- minimum evolution
- balanced minimum evolution
- hierarchical clustering