Abstract
In this paper, we study lower bound techniques for branch-and-bound algorithms for maximum parsimony, with a focus on gene order data. We give a simple O(n 3) time dynamic programming algorithm for computing the maximum circular ordering lower bound, where n is the number of leaves. The well-known gene order phylogeny program, GRAPPA, currently implements two heuristic approximations to this lower bounds. Our experiments show a significant improvement over both these methods in practice. Next, we show that the linear programming-based lower bound of Tang and Moret (Tang and Moret, 2005) can be greatly simplified, allowing us to solve the LP in O * n 3) time in the worst case, and in O *(n 2.5) time amortized over all binary trees. Finally, we formalize the problem of computing the circular ordering lower bound, when the tree topologies are generated bottom-up, as a Path-Constrained Traveling Salesman Problem, and give a polynomial-time 3-approximation algorithm for it. This is a special case of the more general Precedence-Constrained Travelling Salesman Problem and has not previously been studied, to the best of our knowledge.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Moret, B., Wyman, S., Bader, D., Warnow, T., Yan, M.: A new implementation and detailed study of breakpoint analysis. In: PSMB (2001)
Sankoff, D., Blanchette, M.: Multiple genome rearrangement and breakpoint phylogeny. J. Comput. Biol. 5(3), 555–570 (1998)
Bourque, G., Pevzner, P.: Genome-scale evolution: Reconstructing gene orders in the ancestral species. Genome Res. 12(1), 26–36 (2002)
Bryant, D.: A lower bound for the breakpoint phylogeny problem. Journal of Discrete Algorithms 2, 229–255 (2004)
Purdom, P., Bradford, P., Tamura, K., Kumar, S.: Single column discrepency and dynamic max-mini optimizations for quickly finding the most parsimonious evolutionary trees. Bioinformatics 16(2), 140–151 (2000)
Holland, B., Huber, K., Penny, D., Moulton, V.: The minmax squeeze: Guarenteeing a minimal tree for population data. Mol. Biol. and Evol. 22(2), 235–242 (2005)
Tang, J.: A study of bounding methods for reconstructing phylogenies from gene-order data. PhD Thesis (2003)
Tang, J., Moret, B., Cui, L., de Pamphilis, C.: Phylogenetic reconstruction from arbitrary gene-order data. In: BIBE (2004)
Tang, J., Moret, B.: Linear programming for phylogenetic reconstruction based on gene rearrangements. In: CPM (2005)
Moret, B., Tang, J., Warnow, T.: Reconstructing phylogenies from gene-content and gene-order data. In: Gascuel, O. (ed.) Mathematics of Evolution and Phylogeny. Oxford Univ. Press, Oxford (2004)
Chaudhuri, K., Chen, K., Mihaescu, R., Rao, S.: On the tandem duplication-random loss model of genome rearrangement (in review)
Charikar, M., Motwani, R., Raghavan, P., Silverstein, C.: Constrained TSP and low power computing. In: WADS (1997)
Moret, B.: Personal communication (2005)
Lancia, G., Ravi, R.: GESTALT: Genomic steiner alignments. In: CPM (1999)
Young, N.: Sequential and parallel algorithms for mixed packing and covering. In: FOCS (2001)
Flajolet, P., Odlyzko, A.M.: The average height of binary trees and other simple trees. J. Computer System Sci. 25, 171–213 (1982)
Bar-Joseph, Z., Demaine, E.D., Gifford, D.K., Hamel, A.M., Jaakkola, T.S., et al.: K-ary clustering with optimal leaf ordering for gene expression data. Bioinformatics 19(9), 1070–1078 (2003)
Burkard, R.E., Deineko, V.G., Woeginger, G.J.: The travelling salesman and the pq-tree. Mathematics of Operations Research 24, 262–272 (1999)
Farach, M., Kannan, S., Warnow, T.: A robust model for finding optimal evolutionary trees. In: STOC (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bachrach, A., Chen, K., Harrelson, C., Mihaescu, R., Rao, S., Shah, A. (2005). Lower Bounds for Maximum Parsimony with Gene Order Data. In: McLysaght, A., Huson, D.H. (eds) Comparative Genomics. RCG 2005. Lecture Notes in Computer Science(), vol 3678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554714_1
Download citation
DOI: https://doi.org/10.1007/11554714_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28932-6
Online ISBN: 978-3-540-31814-9
eBook Packages: Computer ScienceComputer Science (R0)