Computing phylogenetic roots with bounded degrees and errors is NP-complete

Tatsuie Tsukiji, Zhi-Zhong Chen
2006 Theoretical Computer Science  
In this paper we study the computational complexity of the following optimization problem: given a graph G = (V , E), we wish to find a tree T such that (1) the degree of each internal node of T is at least 3 and at most , (2) the leaves of T are exactly the elements of V, and (3) the number of errors, that is, the symmetric difference between E and {{u, v} : u, v are leaves of T and d T (u, v) k}, is as small as possible, where d T (u, v) denotes the distance between u and v in tree T. We show
more » ... that this problem is NP-hard for all fixed constants , k 3. Let s (k) be the size of the largest clique for which an error-free tree T exists. In the course of our proof, we will determine all trees (possibly with degree 2 nodes) that approximate the (s (k) − 1)-clique by errors at most 2.
doi:10.1016/j.tcs.2006.06.016 fatcat:5bga3s3wkvdxvetl6ifahwq7fe