Finding maximal leaf-agreement isomorphic descendent subtrees from phylogenetic trees with different species

Phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time, in particular molecular sequences. In this paper, we consider two descendent subtree-comparison problems on phylogenetic trees. Given a set of k phylogenetic trees whose leaves are drawn from {1,2,...,n} and the leaves for two arbitrary trees are not necessary the same, we first present a linear-time algorithm to final all the maximal leaf-agreement descendent subtrees. Based on this result, we also present a linear-time algorithm to find all the maximal leaf-agreement isomorphic descendent subtrees.

[1]  Hing-Fung Ting,et al.  An O(nlogn)-time algorithm for the maximum constrained agreement subtree problem for binary trees , 2006, Inf. Process. Lett..

[2]  Jeff Schell,et al.  Cell signalling by oligosaccharides , 1997 .

[3]  Zvi Galil,et al.  Faster tree pattern matching , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[4]  N. Saitou,et al.  The neighbor-joining method: a new method for reconstructing phylogenetic trees. , 1987, Molecular biology and evolution.

[5]  Robert E. Tarjan,et al.  Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..

[6]  Y. Quentin,et al.  Two-component systems in Pseudomonas aeruginosa: why so many? , 2000, Trends in microbiology.

[7]  J. Hoch,et al.  Two-component signal transduction , 1995 .

[8]  Erkki Mäkinen.  On the Subtree Isomorphism Problem for Ordered Trees , 1989, Inf. Process. Lett..

[9]  J. Felsenstein.  Numerical Methods for Inferring Evolutionary Trees , 1982, The Quarterly Review of Biology.

[10]  Amihood Amir,et al.  Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms , 1997, SIAM J. Comput..

[11]  Hans Ulrich Simon,et al.  Pattern matching in trees and nets , 1983, Acta Informatica.

[12]  Paola Bonizzoni,et al.  Approximating the Maximum Isomorphic Agreement Subtree is Hard , 2000, Int. J. Found. Comput. Sci..

[13]  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..

[14]  Gabriel Valiente,et al.  An efficient bottom-up distance between trees , 2001, Proceedings Eighth Symposium on String Processing and Information Retrieval.

[15]  Mikkel Thorup,et al.  An O(n log n) algorithm for the maximum agreement subtree problem for binary trees , 1996, SODA '96.

[16]  Roberto Grossi,et al.  On Finding Commong Subtrees , 1993, Theor. Comput. Sci..

[17]  João Meidanis,et al.  Introduction to computational molecular biology , 1997 .

[18]  W. Fitch.  Toward Defining the Course of Evolution: Minimum Change for a Specific Tree Topology , 1971 .

[19]  Gabriel Valiente,et al.  Algorithms on Trees and Graphs , 2002, Springer Berlin Heidelberg.

[20]  Mikkel Thorup,et al.  Sparse Dynamic Programming for Evolutionary-Tree Comparison , 1997, SIAM J. Comput..

[21]  Olivier Gascuel,et al.  Inferring evolutionary trees with strong combinatorial evidence , 2000, Theor. Comput. Sci..

[22]  K. Strimmer,et al.  Quartet Puzzling: A Quartet Maximum-Likelihood Method for Reconstructing Tree Topologies , 1996 .

[23]  Chuan Yi Tang,et al.  An Improved Algorithm for the Maximum Agreement Subtree Problem , 2004, BIBE.

[24]  W. H. Day.  Optimal algorithms for comparing trees with labeled leaves , 1985 .

[25]  S. Rao Kosaraju,et al.  Efficient tree pattern matching , 1989, 30th Annual Symposium on Foundations of Computer Science.

[26]  Mikkel Thorup,et al.  On the Agreement of Many Trees , 1995, Inf. Process. Lett..

[27]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[28]  Ming-Yang Kao,et al.  An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings , 2001, J. Algorithms.

[29]  Dan Gusfield,et al.  Efficient algorithms for inferring evolutionary trees , 1991, Networks.

[30]  Alon Itai,et al.  On an Algorithm of Zemlyachenko for Subtree Isomorphism , 1999, Inf. Process. Lett..

[31]  Yaw-Ling Lin,et al.  Efficient Algorithms for Descendent Subtrees Comparison of Phylogenetic Trees with Applications to Co-evolutionary Classifications in Bacterial Genome , 2003, ISAAC.