Computing bounded-degree phylogenetic roots of disconnected graphs

  • Authors:

  • Zhi-Zhong Chen;Tatsuie Tsukiji

  • Affiliations:

  • Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan;Department of Information Science, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2006

  • The 3-Steiner root problem

    WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science

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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=