Abstract
The Phylogenetic k th Root Problem (PR k ) is theproblem 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 phylogenetickth root of graph G. The computational complexity of PR k is open, except for k ≤ 4. Recently, Chen et al. investigated PR k 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 connectedG 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.
The full version can be found at http://rnc.r.dendai.ac.jp/~chen/papers/dpr.pdf.
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References
Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (1999)
Chen, Z.-Z., Jiang, T., Lin, G.-H.: Computing phylogenetic roots with bounded degrees and errors. SIAM Journal on Computing 32, 864–879 (2003)
Kearney, P.E., Corneil, D.G.: Tree powers. Journal of Algorithms 29, 111–131 (1998)
Lin, G., Kearney, P.E., Jiang, T.: Phylogenetic k-root and steiner k-root. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 539–551. Springer, Heidelberg (2000)
Lin, Y.-L., Skiena, S.S.: Algorithms for square roots of graphs. SIAM Journal on Discrete Mathematics 8, 99–118 (1995)
Motwani, R., Sudan, M.: Computing roots of graphs is hard. Discrete Applied Mathematics 54, 81–88 (1994)
Nishimura, N., Ragde, P., Thilikos, D.M.: On graph powers for leaf-labeled trees. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 125–138. Springer, Heidelberg (2000)
Swofford, D.L., Olsen, G.J., Waddell, P.J., Hillis, D.M.: Phylogenetic inference. In: Hillis, D.M., Moritz, C., Mable, B.K. (eds.) Molecular Systematics, 2nd edn., pp. 407–514. Sinauer Associates, Sunderland (1996)
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Chen, ZZ., Tsukiji, T. (2004). Computing Bounded-Degree Phylogenetic Roots of Disconnected Graphs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_26
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DOI: https://doi.org/10.1007/978-3-540-30559-0_26
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