This Article 
 Bibliographic References 
 Add to: 
Linear-Time Algorithms for the Multiple Gene Duplication Problems
January-February 2011 (vol. 8 no. 1)
pp. 260-265
Cheng-Wei Luo, National Taiwan University, Taipei
Ming-Chiang Chen, National Taiwan University, Taipei
Yi-Ching Chen, National Taiwan University, Taipei
Roger W.L. Yang, National Taiwan University, Taipei
Hsiao-Fei Liu, National Taiwan University, Taipei
Kun-Mao Chao, National Taiwan University, Taipei
A fundamental problem arising in the evolutionary molecular biology is to discover the locations of gene duplications and multiple gene duplication episodes based on the phylogenetic information. The solutions to the MULTIPLE GENE DUPLICATION problems can provide useful clues to place the gene duplication events onto the locations of a species tree and to expose the multiple gene duplication episodes. In this paper, we study two variations of the MULTIPLE GENE DUPLICATION problems: the EPISODE-CLUSTERING (EC) problem and the MINIMUM EPISODES (ME) problem. For the EC problem, we improve the results of Burleigh et al. with an optimal linear-time algorithm. For the ME problem, on the basis of the algorithm presented by Bansal and Eulenstein, we propose an optimal linear-time algorithm.

[1] M.S. Bansal, J.G. Burleigh, O. Eulenstein, and A. Wehe, "Heuristics for the Gene-Duplication Problem: A $\Theta (n)$ Speed-Up for the Local Search," Proc. 11th Int'l Conf. Research in Computational Molecular Biology, pp. 238-252, 2007.
[2] M.S. Bansal and O. Eulenstein, "An $\Omega (n^2/\log n)$ Speed-Up of TBR Heuristics for the Gene-Duplication Problem," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 5, no. 4, pp. 514-524, Oct.-Dec. 2008.
[3] M.S. Bansal and O. Eulenstein, "The Multiple Gene Duplication Problem Revisited," Bioinformatics, vol. 24, no. 13, pp. i132-i138, 2008.
[4] M.S. Bansal and O. Eulenstein, "The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI Based Local Searches," Proc. Fourth Int'l Symp. Bioinformatics Research and Applications, pp. 14-25, 2008.
[5] M.A. Bender and M. Farach-Colton, "The LCA Problem Revisited," Proc. Fourth Latin Am. Theoretical Informatics Symp., pp. 88-94, 2000.
[6] J.G. Burleigh, M.S. Bansal, A. Wehe, and O. Eulenstein, "Locating Multiple Gene Duplications through Reconciled Trees," Proc. 12th Ann. Int'l Conf. Research in Computational Molecular Biology, pp. 273-284, 2008.
[7] M. Goodman, J. Czelusniak, G.W. Moore, A.E. Romero-Herrera, and G. Matsuda, "Fitting the Gene Lineage into Its Species Lineage, a Parsimony Strategy Illustrated by Cladograms Constructed from Globin Sequences," Systematic Zoology, vol. 28, pp. 132-163, 1979.
[8] R. Guigó, I. Muchnik, and T.F. Smith, "Reconstruction of Ancient Molecular Phylogeny," Molecular Phylogenetics and Evolution, vol. 6, no. 2, pp. 189-213, 1996.
[9] B. Ma, M. Li, and L. Zhang, "From Gene Trees to Species Trees," SIAM J. Computing, vol. 30, no. 3, pp. 729-752, 2000.
[10] J.E. Neigel and J.C. Avise, "Phylogenetic Relationship of Mitochondrial DNA under Various Demographic Models of Speciation," Evolutionary Processes and Theory, pp. 515-534, Academic Press, 1986.
[11] R.D.M. Page and J.A. Cotton, "Vertebrate Phylogenomics: Reconciled Trees and Gene Duplications," Proc. Seventh Pacific Symp. Biocomputing, pp. 536-547, 2002.
[12] P. Pamilo and M. Nei, "Relationship between Gene Trees and Species Trees," Molecular Biology and Evolution, vol. 5, pp. 568-583, 1988.
[13] N. Takahata, "Gene Genealogy in Three Related Populations: Consistency Probability between Gene and Population Trees," Genetics, vol. 122, pp. 957-966, 1989.
[14] C.I. Wu, "Inference of Species Phylogeny in Relation to Segregation of Ancient Polymorphisms," Genetics, vol. 127, pp. 429-435, 1991.
[15] L. Zhang, "On a Mirkin-Muchnik-Smith Conjecture for Comparing Molecular Phylogenies," J. Computational Biology, vol. 4, no. 2, pp. 177-187, 1997.

Index Terms:
Computational phylogenetics, gene duplication, computations on discrete structures, linear-time algorithm.
Cheng-Wei Luo, Ming-Chiang Chen, Yi-Ching Chen, Roger W.L. Yang, Hsiao-Fei Liu, Kun-Mao Chao, "Linear-Time Algorithms for the Multiple Gene Duplication Problems," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 1, pp. 260-265, Jan.-Feb. 2011, doi:10.1109/TCBB.2009.52
Usage of this product signifies your acceptance of the Terms of Use.