Computing bounded-degree phylogenetic roots of disconnected graphs

Authors:
Zhi-Zhong Chen;Tatsuie Tsukiji
Affiliations:
Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama, Japan;Department of Information Science, Tokyo Denki University, Hatoyama, Saitama, Japan
Venue:
Journal of Algorithms
Year:
2006

Citing 4
Cited 2

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Abstract

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.