Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Nearest Neighbor Interchange and Related Distances

  • Bhaskar DasGupta
  • Xin He
  • Ming Li
  • John Tromp
  • Louxin Zhang
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_256

Years and Authors of Summarized Original Work

  • 1997; DasGupta, He, Jiang, Li, Tromp, Zhang

Problem Definition

In this entry, the authors state results on some transformation-based distances for evolutionary trees. Several distance models for evolutionary trees have been proposed in the literature. Among them, the best known is perhaps the nearest neighbor interchange (nni) distance introduced independently in [ 10] and [ 9]. The authors will focus on the nni distance and a closely related distance called the subtree-transfer distance originally introduced in [ 5, 6]. Several papers that involved DasGupta, He, Jiang, Li, Tromp, and Zhang essentially showed the following results:
  • A correspondence between the nni distance and the linear-cost subtree-transfer distance on unweighted trees.

  • Computing the nni distance is NP-hard, but admits a fixed-parameter tractability and a logarithmic ratio approximation algorithms.

  • A 2-approximation algorithm for the linear-cost subtree-transfer distance on...

Keywords

Comparison of phylogenies Network models of evolution 
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Recommended Reading

  1. 1.
    DasGupta B, He X, Jiang T, Li M, Tromp J, Zhang L (1997) On distances between phylogenetic trees. In: 8th annual ACM-SIAM symposium on discrete algorithms, New Orleans, pp 427–436Google Scholar
  2. 2.
    DasGupta B, He X, Jiang T, Li M, Tromp J, Wang L, Zhang L (1998) Computing distances between evolutionary trees. In: Du DZ, Pardalos PM (eds) Handbook of combinatorial optimization, vol 2. Kluwer Academic, Norwell, pp 35–76Google Scholar
  3. 3.
    DasGupta B, He X, Jiang T, Li M, Tromp J (1999) On the linear-cost subtree-transfer distance. Algorithmica 25(2):176–195MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    DasGupta B, He X, Jiang T, Li M, Tromp J, Zhang L (2000) On computing the nearest neighbor interchange distance. In: Du DZ, Pardalos PM, Wang J (eds) Proceedings of the DIMACS workshop on discrete problems with medical applications. DIMACS series in discrete mathematics and theoretical computer science, vol 55. American Mathematical Society, Providence, Rhode Island, USA, pp 125–143Google Scholar
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    Hein J (1990) Reconstructing evolution of sequences subject to recombination using parsimony. Math Biosci 98:185–200MathSciNetCrossRefzbMATHGoogle Scholar
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    Hein J (1993) A heuristic method to reconstruct the history of sequences subject to recombination. J Mol Evol 36:396–405CrossRefGoogle Scholar
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    Hein J, Jiang T, Wang L, Zhang K (1996) On the complexity of comparing evolutionary trees. Discret Appl Math 71:153–169MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kuhner M, Felsenstein J (1994) A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates. Mol Biol Evol 11(3):459–468Google Scholar
  9. 9.
    Moore GW, Goodman M, Barnabas J (1973) An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets. J Theor Biol 38:423–457CrossRefGoogle Scholar
  10. 10.
    Robinson DF (1971) Comparison of labeled trees with valency three. J Comb Theory Ser B 11:105–119MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Bhaskar DasGupta
    • 1
  • Xin He
    • 2
  • Ming Li
    • 3
  • John Tromp
    • 4
  • Louxin Zhang
    • 5
  1. 1.Department of Computer Science, University of IllinoisChicagoUSA
  2. 2.Department of Computer Science and Engineering, The State University of New YorkBuffaloUSA
  3. 3.David R. Cheriton School of Computer Science, University of WaterlooWaterlooCanada
  4. 4.CWIAmsterdamNetherlands
  5. 5.Department of Mathematics, National University of SingaporeSingaporeSingapore