Abstract
The Degree-ΔClosest Phylogenetic k th Root Problem (ΔCPR k ) is the problem of finding a (phylogenetic) tree T from a given graph G=(V,E) such that (1) the degree of each internal node of T is at least 3 and at most Δ, (2) the external nodes (i.e. leaves) of T are exactly the elements of V, and (3) the number of disagreements, |E ⊕ {{u,v} : u,v are leaves of T and d T (u,v) ≤ k}| does not exceed a given number, where d T (u,v) denotes the distance between u and v in tree T. We show that this problem is NP-hard for all fixed constants Δ,k ≥ 3.
Our major technical contribution is the determination of all pylogenetic roots that approximate the almost largest cliques. Specifically, let s Δ(k) be the size of a largest clique having a kth phylogenetic root with maximum degree Δ. We determine all the phylogenic kth roots with maximum degree Δ that approximate the (s Δ(k)–1)-clique within error 2, where we allow the internal nodes of phylogeny to have degree 2.
Supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 14580390.
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Tsukiji, T., Chen, ZZ. (2004). Computing Phylogenetic Roots with Bounded Degrees and Errors Is Hard. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_48
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DOI: https://doi.org/10.1007/978-3-540-27798-9_48
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