Computing Bounded-Degree Phylogenetic Roots of Disconnected Graphs

The Phylogenetic kth Root Problem (PRk) is the problem of finding a (phylogenetic) tree T from a given graph G = (V, E) such that (1) T has no degree-2 internal nodes, (2) the external nodes (i.e. leaves) of T are exactly the elements of V , and (3) (u, v) ∈ E if and only if the distance between u and v in tree T is at most k, where k is some fixed threshold k. Such a tree T, if exists, is called a phylogenetic kth root of graph G. The computational complexity of PRk is open, except for k ≤ 4. Recently, Chen et al. investigated PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant. They presented a linear-time algorithm that determines if a given connected G has such a phylogenetic kth root, and if so, demonstrates one. In this paper, we supplement their work by presenting a linear-time algorithm for disconnected graphs. Keywords. Phylogeny, phylogenetic root, computational biology, graph power, tree power, graph alg...

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Zhi-Zhong Chen, Tatsuie Tsukiji
• Keywords: Computer Science, Kth Root Problem, Phylogenetic Kth Root, Phylogenetic Root, WG 2004