BibTeX
@MISC{09anote,
author = {},
title = {A Note on Minimum Flip Consensus and Maximum Compatible Subset},
year = {2009}
}
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Abstract
Abstract. Minimum Flip Consensus is a supertree method introduced in 2002 [CEFBS02, CDE+03, CEFBS06, CEFBB06, BBT08, KU08], which aims at performing the smallest number of changes (taxa deletion or addition) in a set of clusters so that it becomes compatible with a tree. There exist FPT algorithms [CEFBS02, BBT08, KU08], fixed ratio approximation schemes [CEFBS02], and heuris-tics [CEFBB06] to solve this problem, which can be coded as an edge-editing problem to transform a bipartite graph into an “M-free graph ” [CEFBS02]. Maximum Compatible Subset removes the min-imum number t of taxa so that the cluster set on the remaining taxa becomes compatible with a tree [HRB+09]. This problem can be coded as a vertex-deletion problem to transform a bipartite graph into an M-free graph. 1 Coding Maximum Compatible Subset as an M-free graph editing problem Definition 1.1 (character graph). Let C = {C1,..., Cr} be a set of clusters on the set X of n leaves. The character graph of C is the bipartite graph G(C) = (C, X,E), and E = {{x,Ci}|x ∈ Ci}. Definition 1.2 (M-free graph property). An M-graph is a cycle-free path of length 4. A bipar-tite graph G = (X,Y,E) is an M-free graph if it does not have an induced M-graph whose degree-1 nodes are in Y. Note that an incompatibility of two clusters C1 and C2 of C forces the existence of three taxa x, y and z such that x ∈ C1 \ C2, y ∈ C1 ∩ C2, z ∈ C2 \ C1, which corresponds exactly to the presence of an induced M-graph with three taxa vertices in the character graph of C, as illustrated
Keyphrases
maximum compatible subset minimum flip consensus bipartite graph character graph m-free graph induced m-graph c1 c2 edge-editing problem taxon deletion vertex-deletion problem ci ci m-free graph cefbs02 min-imum number supertree method problem definition ratio approximation scheme cluster c1 taxon vertex cycle-free path degree-1 node tree hrb fpt algorithm cefbs02 m-free graph property bipar-tite graph c2 c1 heuris-tics cefbb06
