Abstract
This paper addresses the informational asymmetry for constructing an ultrametric evolutionary tree from upper and lower bounds on pairwise distances between n given species. We show that the tallest ultrametric tree exists and can be constructed in O(n 2) time, while the existence of the shortest ultrametric tree depends on whether the lower bounds are ultrametric. The tallest tree construction algorithm gives a very simple solution to the construction of an ultrametric tree. We also provide an efficient O(n 2)-time algorithm for checking the uniqueness of an ultrametric tree, and study a query problem for testing whether an ultrametric tree satisfies both upper and lower bounds.
Supported in part by the Lipper Foundation.
Supported in part by NSF Grant 9531028.
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
J.-P. Barthélémy and A. Guénoche. Trees and proximity representations. Wiley-Interscience Series in Discrete Mathematics and Optimization.Wiley, New York, NY, 1991. 250
V. Berry and O. Gascuel. Inferring evolutionary trees with strong combinatorial evidence. In T. Jiang and D. T. Lee, editors, Lecture Notes in Computer Science 1276: Proceedings of the 3rd Annual International Computing and Combinatorics Conference, pages 111–123. Springer-Verlag, New York, NY, 1997. 248
J. C. Culbertson and P. Rudnicki. A fast algorithm for constructing trees from distance matrices. Information Processing Letters, 30(4):215–220, 1989. 248
M. Farach, S. Kannan, and T. Warnow. A robust model for finding optimal evolutionary trees. Algorithmica, 13(1/2):155–179, 1995. 249, 249, 250
D. Gusfield. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, New York, NY, 1997. 248
J. J. Hein. An optimal algorithm to reconstruct trees from additive distance data. Bulletin of Mathematical Biology, 51:597–603, 1989. 248
D. M. Hillis, C. Moritz, and B. K. Mable, editors. Molecular Systematics. Sinauer Associates, Sunderland, Ma, 2nd edition, 1996. 248
J. C. Setubal and J. Meidanis. Introduction to Computational Molecular Biology. PWS Publishing Company, Boston, MA, 1997. 248, 248, 250
M. S. Waterman. Introduction to Computational Biology: Maps, Sequences and Genomes. Chapman & Hall, New York, NY, 1995. 248
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, T., Kao, MY. (1999). On the Informational Asymmetry between Upper and Lower Bounds for Ultrametric Evolutionary Trees. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_22
Download citation
DOI: https://doi.org/10.1007/3-540-48481-7_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66251-8
Online ISBN: 978-3-540-48481-3
eBook Packages: Springer Book Archive