Linear time construction of 5-phylogenetic roots for tree chordal graphs

William S. Kennedy (), Hui Kong, Guohui Lin () and Guiying Yan ()
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William S. Kennedy: McGill University
Hui Kong: Academy of Mathematics and Systems Science
Guohui Lin: University of Alberta
Guiying Yan: Academy of Mathematics and Systems Science

Journal of Combinatorial Optimization, 2010, vol. 19, issue 1, No 8, 94-106

Abstract: Abstract Inspired by phylogenetic tree construction in computational biology, Lin et al. (The 11th Annual International Symposium on Algorithms and Computation (ISAAC 2000), pp. 539–551, 2000) introduced the notion of a k -phylogenetic root. A k-phylogenetic root of a graph G is a tree T such that the leaves of T are the vertices of G, two vertices are adjacent in G precisely if they are within distance k in T, and all non-leaf vertices of T have degree at least three. The k-phylogenetic root problem is to decide whether such a tree T exists for a given graph G. In addition to introducing this problem, Lin et al. designed linear time constructive algorithms for k≤4, while left the problem open for k≥5. In this paper, we partially fill this hole by giving a linear time constructive algorithm to decide whether a given tree chordal graph has a 5-phylogenetic root; this is the largest class of graphs known to have such a construction.

Keywords: Graph algorithms; Phylogenetic roots; Leaf roots; Steiner roots; Chordal graphs; Linear time recognition (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10878-008-9164-y

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