The agreement problem for unrooted phylogenetic trees is FPT

A collectionT of k unrooted phylogenetic trees on dierent leaf sets is said to be strictly compatible or in agreement if there exists a tree T such that each tree inT can be obtained from T by deleting leaves and suppressing degree-2 vertices. The problem of determining if a set of unrooted trees is in agreement has been proved NP-hard in 1992. Here, we show that an f(k) n algorithm exists, for some computable function f of k, proving that strict compatibility of unrooted phylogenetic trees is xed-parameter

[1]  A. Bauer,et al.  Between a rock and a hard polytomy: rapid radiation in the rupicolous girdled lizards (Squamata: Cordylidae). , 2011, Molecular phylogenetics and evolution.

[2]  M. Steel.  The complexity of reconstructing trees from qualitative characters and subtrees , 1992 .

[3]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs , 1990, Inf. Comput..

[4]  W. Maddison.  RECONSTRUCTING CHARACTER EVOLUTION ON POLYTOMOUS CLADOGRAMS , 1989, Cladistics : the international journal of the Willi Hennig Society.

[5]  Alfred V. Aho,et al.  Inferring a Tree from Lowest Common Ancestors with an Application to the Optimization of Relational Expressions , 1981, SIAM J. Comput..

[6]  Ole Seehausen,et al.  African cichlid fish: a model system in adaptive radiation research , 2006, Proceedings of the Royal Society B: Biological Sciences.

[7]  Detlef Seese,et al.  Easy Problems for Tree-Decomposable Graphs , 1991, J. Algorithms.

[8]  Hans L. Bodlaender,et al.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

[9]  David Bryant,et al.  Compatibility of unrooted phylogenetic trees is FPT , 2006, Theor. Comput. Sci..

[10]  Steven Poe,et al.  BIRDS IN A BUSH: FIVE GENES INDICATE EXPLOSIVE EVOLUTION OF AVIAN ORDERS , 2004, Evolution; international journal of organic evolution.

[11]  Nicholas C. Wormald,et al.  Reconstruction of Rooted Trees From Subtrees , 1996, Discret. Appl. Math..