Abstract
I describe and compare three distance measures defined on labeled binary trees: the contraction metric of Bourque(1978), the crossover or nearest neighbor interchange metric of Robinson(1971), and the closest partitions distance measure of Waterman and Smith(1978). Since the results of this survey are not altogether satisfactory, I suggest several directions that research in this area may take.
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References
Boland, R. P. 1982. Determining distances between labeled binary trees. B.Sc. Honours Thesis. Dept. of Computer Science, Memorial Univ. of Newfoundland, St. John’s, Nfld., Canada.
Boland, R. P., E. K. Brown, and W. H. E. Day. 1982. Approximating minimum-length-sequence metrics: a cautionary note. Mathematical Social Sciences (to appear).
Boorman, S. A., and D. C. Olivier, 1973. Metrics on spaces of finite trees. J. Math. Psychol. 10: 26–59.
Bourque, M. 1978. Arbres de Steiner et reseaux dont certains sommets sont a localisation variable. Ph.D. Thesis. Universite de Montreal, Montreal, Quebec, Canada.
Brown, E. K. 1982. Some closest partitions distances between trees. B.Sc. Honours Thesis. Dept. of Computer Science, Memorial Univ. of Newfoundland, St. John’s, Nfld., Canada.
Culik II, K., and D. Wood. 1982. A note on some similarity measures. Information Processing Letters (to appear).
Day, W. H. E. 1981. The complexity of computing metric distances between partitions. Mathematical Social Sciences 1: 269–287.
Day, W. H. E. 1982. Properties of the nearest neighbor interchange metric for trees of small size. Dept. of Computer Science Tech. Rep. 8203. Memorial Univ. of Newfoundland, St. John’s, Nfld., Canada.
Goodman, N. 1951. The Structure of Appearance. Harvard Univ. Press, Cambridge, Massachusetts, U.S.A.
Jarvis, J. P., J. K. Luedeman, and D. R. Shier. 1981. Comments on computing the similarity of binary trees. Dept. of Mathematical Sciences Tech. Rep. 373. Clemson Univ., Clemson, South Carolina, U.S.A.
Jarvis, J. P., J. K. Luedeman, and D. R. Shier. 1982. A counterexample in measuring the distance between binary trees. Dept. of Mathematical Sciences, Clemson Univ., Clemson, South Carolina, U.S.A.
Monjardet, B. 1981. Metrics on partially ordered sets - a survey. Discr. Math. 35: 173–184.
Moore, G. W., M. Goodman, and J. Barnabas. 1973. An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets. J. theor. Biol. 38: 423–457.
Penny, D., L. R. Foulds, and M. D. Hendy. 1982. Testing the theory of evolution by comparing phylogenetic trees constructed from five different protein sequences. Nature, 20 May 1982, 297: 197–200.
Restle, F. 1959. A metric and an ordering on sets. Psychometrika 24: 207–220.
Robinson, D. F. 1971. Comparison of labeled trees with valency three. J. Comb. Th. 11: 105–119.
Robinson, D. F., and L. R. Foulds. 1981. Comparison of phylogenetic trees. Math. Biosci. 53: 131–147.
Waterman, M. S., and T. F. Smith. 1978. On the similarity of dendrograms. J. theor. Biol. 73: 789–800.
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© 1983 Springer-Verlag Berlin Heidelberg
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Day, W.H.E. (1983). Distributions of Distances between Pairs of Classifications. In: Felsenstein, J. (eds) Numerical Taxonomy. NATO ASI Series, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69024-2_19
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DOI: https://doi.org/10.1007/978-3-642-69024-2_19
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