Abstract
Comparing objects to find their similarities or, equivalently, dissimilarities, is a fundamental issue in many fields including pattern recognition, image analysis, drug design, the study of thermodynamic costs of computing, cognitive science, etc. Various models have been introduced to measure the degree of similarity or dissimilarity in the literature. In the latter case the degree of dissimilarity is also often referred to as the distance. While some distances are straightforward to compute, e.g. the Hamming distance for binary strings, the Euclidean distance for geometric objects; some others are formulated as combinatorial optimization problems and thus pose nontrivial challenging algorithmic problems, sometimes even uncomputable, such as the universal information distance between two objects [4].
Supported in part by a CGAT (Canadian Genome Analysis and Technology) grant. Work done while the author was at McMaster University and University of Waterloo.
Supported in part by NSF grant 9205982 and CGAT.
Supported in part by NSERC Operating Grant OGP0046613 and CGAT.
Supported in part by the NSERC Operating Grant OGP0046506 and CGAT.
Supported in part by CGAT and NSERC Internation Fellowship.
Supported in part by Hong Kong Research Council.
Supported in part by CGAT.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Aldous, Triangulating the circle, at random. Amer Math. Monthly, 89, pp. 223–234, 1994.
M.A. Armstrong, Groups and Symmetry, Springer Verlag, New York Inc., 1988.
D. Barry and J.A. Hartigan, Statistical analysis of hominoid molecular evolution, Stat. Sci., 2, pp. 191–210, 1987.
C.H. Bennett, P. Gács, M. Li, P. Vitányi, and W. Zurek, Information Distance, to appear in IEEE Trans. Inform. Theory.
R. P. Boland, E. K. Brown and W. H. E. Day, Approximating minimumlength-sequence metrics: a cautionary note, Math. Soc. Sci., 4, pp. 261–270, 1983.
K. Culik II and D. Wood, A note on some tree similarity measures, Inform. Proc. Let., 15, pp. 39–42, 1982.
B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp and L. Zhang, On distances between phylogenetic trees, Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 427–436, 1997.
B. DasGupta, X. He, T. Jiang, M. Li, and J. Tromp, On the linear-cost subtree-transfer distance, Algorithmica, submitted, 1997.
B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang, On computing the nearest neighbor interchange distance, Preprint, 1997.
W. H. E. Day, Properties of the nearest neighbor interchange metric for trees of small size, Journal of Theoretical Biology, 101, pp. 275–288, 1983.
A. K. Dewdney, Wagner’s theorem for torus graphs, Discrete Math., 4, pp. 139–149, 1973.
A.W.F. Edwards and L.L. Cavalli-Sforza, The reconstruction of evolution, Ann. Hum. Genet., 27, 105, 1964. (Also in Heredity 18, 553.)
J. Felsenstein, Evolutionary trees for DNA sequences: a maximum likelihood approach. J. Mol. Evol., 17, pp. 368–376, 1981.
J. Felsenstein, personal communication, 1996.
W.M. Fitch, Toward defining the course of evolution: minimum change for a specified tree topology, Syst. Zool., 20, pp. 406–416, 1971.
W.M. Fitch and E. Margoliash, Construction of phylogenetic trees, Science, 155, pp. 279–284, 1967.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979.
L. Guibas and J. Hershberger, Morphing simple polygons, Proceeding of the ACM 10th Annual Sym. of Comput. Geometry, pp. 267–276, 1994.
J. Hein, Reconstructing evolution of sequences subject to recombination using parsimony, Math. Biosci., 98, pp. 185–200, 1990.
J. Hein, A heuristic method to reconstruct the history of sequences subject to recombination, J. Mol. Evol., 36, pp. 396–405, 1993.
J. Hein, personal email communication, 1996.
J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics, 71, pp. 153–169, 1996.
J. Hershberger and S. Suri, Morphing binary trees. Proceeding of the ACM-SIAM 6th Annual Symposium of Discrete Algorithms, pp. 396–404, 1995.
F. Hurtado, M. Noy, and J. Urrutia, Flipping edges in triangulations, Proc. of the ACM 12th Annual Sym. of Comput. Geometry, pp. 214–223, 1996.
J. P. Jarvis, J. K. Luedeman and D. R. Shier, Counterexamples in measuring the distance between binary trees, Mathematical Social Sciences, 4, pp. 271–274, 1983.
J. P. Jarvis, J. K. Luedeman and D. R. Shier, Comments on computing the similarity of binary trees, Journal of Theoretical Biology, 100, pp. 427–433, 1983.
J. Kececioglu and D. Gusfield, Reconstructing a history of recombinations from a set of sequences, Proc. 5th Annual ACM-SIAM Symp. Discrete Algorithms, 1994.
M. Kuhner and J. Felsenstein, A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates. Mol. Biol. Evol.11 (3), pp. 459–468, 1994.
M. Krivânek, Computing the nearest neighbor interchange metric for unlabeled binary trees is NP-complete, Journal of Classification, 3, pp. 55–60, 1986.
V. King and T. Warnow, On Measuring the nni distance between two evolutionary trees, DIMACS mini workshop on combinatorial structures in molecular biology, Rutgers University, Nov 4, 1994.
S. Khuller, Open Problems: 10, SIGACT News, 24 (4), p. 46, Dec 1994.
W.J. Le Quesne, The uniquely evolved character concept and its cladistic application, Syst. Zool., 23, pp. 513–517, 1974.
M. Li, J. Tromp, and L.X. Zhang, On the nearest neighbor interchange distance between evolutionary trees, Journal of Theoretical Biology, 182, pp. 463–467, 1996.
M. Li and L. Zhang, Better Approximation of Diagonal-Flip Transformation and Rotation Transformation, Manuscript, 1997.
G. W. Moore, M. Goodman and J. Barnabas, An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets, Journal of Theoretical Biology, 38, pp. 423–457, 1973.
J. Pallo, On rotation distance in the lattice of binary trees, Infor. Proc. Letters, 25, pp. 369–373, 1987.
D. F. Robinson, Comparison of labeled trees with valency three, Journal of Combinatorial Theory,Series B, 11, pp. 105–119, 1971.
N. Saitou and M. Nei, The neighbor-joining method: a new method for reconstructing phylogenetic trees, Mol. Biol. Evol., 4, pp. 406–425, 1987.
D. Sankoff, Minimal mutation trees of sequences, SIAM J. Appl. Math., 28, pp. 35–42, 1975.
D. Sankoff and J. Kruskal (Eds), Time Warps, String Edits, and Macromolecules: the Theory and Practice of Sequence Comparison, Addison Wesley, Reading Mass., 1983.
D. Sleator, R. Tarjan, W. Thurston, Rotation distance, triangulations, and hyperbolic geometry, J. Amer. Math. Soc., 1, pp. 647–681, 1988.
D. Sleator, R. Tarjan, W. Thurston, Short encodings of evolving structures, SIAM J. Discr. Math., 5, pp. 428–450, 1992.
K.C. Tai, The tree-to-tree correction problem, J. ACM, 26, pp. 422–433, 1979.
A. von Haseler and G.A. Churchill, Network models for sequence evolution, J. Mol. Evol., 37, pp. 77–85, 1993.
K. Wagner, Bemerkungen zum vierfarbenproblem, J. Deutschen Math.Verin., 46, pp. 26–32, 1936.
M. S. Waterman, Introduction to computational biology: maps, sequences and genomes, Chapman Sc Hall, 1995.
M. S. Waterman and T. F. Smith, On the similarity of dendrograms, Journal of Theoretical Biology, 73, pp. 789–800, 1978.
K. Zhang and D. Shasha, Simple fast algorithms for the editing distance between trees and related problems, SIAM J. Comput. 18, pp. 12451–262, 1989.
K. Zhang, J. Wang and D. Sasha, On the editing distance between undirected acyclic graphs, International J. of Foundations of Computer Science 7 (13), March 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Kluwer Academic Publishers
About this chapter
Cite this chapter
DasGupta, B. et al. (1998). Computing Distances between Evolutionary Trees. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0303-9_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7987-4
Online ISBN: 978-1-4613-0303-9
eBook Packages: Springer Book Archive