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Untangling Tanglegrams: Comparing Trees by Their Drawings

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Book cover Bioinformatics Research and Applications (ISBRA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5542))

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Abstract

A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in biology – to compare evolutionary histories of host and parasite species and to analyze genes of species in the same geographical area. We consider optimizations problems in tanglegram drawings. We show a linear time algorithm to decide if a tanglegram admits a planar embedding by a reduction to the planar graph drawing problem. This problem was considered by Fernau, Kauffman and Poths. (FSTTCS 2005). Our reduction method provides a simpler proof and helps to solve a conjecture they posed, showing a fixed-parameter tractable algorithm for minimizing the number of crossings over all d-ary trees.

For the case where one tree is fixed, we show an O(n logn) algorithm to determine the drawing of the second tree that minimizes the number of crossings. This improves the bound from earlier methods. We introduce a new optimization criterion using Spearman’s footrule optimization and give an O(n 2) algorithm.

We also show integer programming formulations to quickly obtain tanglegram drawings that minimize the two optimization measures discussed. We prove lower bounds on the maximum gap between the optimal solution and the heuristic of Dwyer and Schreiber (Austral. Symp. on Info. Vis. 2004) to minimize crossings.

This research was partially supported by NSF grants SEI-BIO 0513910, SEI-SBE 0513660, CCF-0515378, and IIS-0803564.

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References

  1. Bansal, M.S., Chang, W.-C., Eulenstein, O., Fernández-Baca, D.: Generalized binary tanglegrams: Algorithms and applications. In: BiCoB (2009)

    Google Scholar 

  2. Bertolazzi, P., Battista, G.D., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. Comput. 27(1), 132–169 (1998)

    Article  Google Scholar 

  3. Biedl, T.C., Brandenburg, F.-J., Deng, X.: Crossings and permutations. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 1–12. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Buchin, K., Buchin, M., Byrka, J., Nöllenburg, M., Okamoto, Y., Silveira, R.I., Wolff, A.: Drawing (complete) binary tanglegrams: Hardness, approximation, fixed-parameter tractability. In: Graph Drawing. Springer, Heidelberg (2008)

    Google Scholar 

  5. Burt, A., Trivers, R.: Genes in Conflict. Belknap Harvard Press (2006)

    Google Scholar 

  6. Charleston, M., Perkins, S.: Lizards, malaria, and jungles in the Caribbean. In: Page, R. (ed.) Tangled Trees: Phylogeny, Cospeciation, and Coevolution, pp. 65–92. University Of Chicago Press, Chicago (2003)

    Google Scholar 

  7. Diaconis, P., Graham, R.L.: Spearman’s footrule as a measure of disarray. Journal of the Royal Statistical Society. Series B (Methodological) 39(2), 262–268 (1977)

    Google Scholar 

  8. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: WWW, pp. 613–622 (2001)

    Google Scholar 

  9. Dwyer, T., Schreiber, F.: Optimal leaf ordering for two and a half dimensional phylogenetic tree visualisation. In: Australasian Symp. on Info. Vis., pp. 109–115 (2004)

    Google Scholar 

  10. Page, R.D.M. (ed.): Tangled Trees: Phylogeny, Cospeciation, and Coevolution. University Of Chicago Press, Chicago (2002)

    Google Scholar 

  11. Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. In: SODA, pp. 28–36 (2003)

    Google Scholar 

  12. Fernau, H., Kaufmann, M., Poths, M.: Comparing trees via crossing minimization. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 457–469. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Foulds, L.R., Graham, R.L.: The Steiner problem in phylogeny is NP-complete. Adv. in Appl. Math. 3(1), 43–49 (1982)

    Article  Google Scholar 

  14. Garey, M., Johnson, D.S.: Crossing number is np-complete. SIAM Journal on Algebraic and Discrete Methods 4, 312–316 (1983)

    Article  Google Scholar 

  15. Hinze, R., Paterson, R.: Finger trees: A simple general-purpose data structure. Journal of Functional Programming 16(2), 197–217 (2006)

    Article  Google Scholar 

  16. Hopcroft, J.E., Tarjan, R.E.: Efficient planarity testing. J. ACM 21(4), 549–568 (1974)

    Article  Google Scholar 

  17. Huelsenbeck, J.P., Ronquist, F.: Mrbayes: Bayesian inference of phylogeny (2001)

    Google Scholar 

  18. Kaplan, H., Tarjan, R.E.: Purely functional representations of catenable sorted lists. In: STOC 1996, pp. 202–211. ACM, New York (1996)

    Google Scholar 

  19. Kawarabayashi, K., Reed, B.: Computing crossing number in linear time. In: STOC, pp. 382–390 (2007)

    Google Scholar 

  20. Lee, J.: All-different polytopes. Journal of Combin. Optim. 6(3), 335–352 (2002)

    Article  Google Scholar 

  21. Lozano, A., Pinter, R.Y., Rokhlenko, O., Valiente, G., Ziv-Ukelson, M.: Seeded tree alignment and planar tanglegram layout. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 98–110. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Hillis, D.M., Heath, T., John, K.S.: Analysis and visualization of tree space. Systematic Biology 3, 471–482 (2005)

    Article  Google Scholar 

  23. Nöllenburg, M., Holten, D., Völker, M., Wolff, A.: Drawing binary tanglegrams: An experimental evaluation. In: ALENEX, pp. 106–119. SIAM, Philadelphia (2009)

    Google Scholar 

  24. Roch, S.: A short proof that phylogenetic tree reconstruction by maximum likelihood is hard. IEEE/ACM Trans. Comp. Biol. and Bioinf. 3(1), 92–94 (2006)

    Article  Google Scholar 

  25. Shih, W.K., Hsu, W.-L.: A new planarity test. Theor. Comput. Sci. 223(1-2), 179–191 (1999)

    Article  Google Scholar 

  26. Swofford, D.L.: PAUP*. Phylogenetic Analysis Using Parsimony (*and Other Methods). Version 4. Sinauer Associates, Sunderland, Massachusetts (2002)

    Google Scholar 

  27. Swofford, D.L., Olsen, G.J., Waddell, P.J., Hillis, D.M.: Phylogenetic inference. In: Molecular Systematics, 2nd edn., pp. 407–514. Sinauer (1996)

    Google Scholar 

  28. Venkatachalam, B., Apple, J., John, K.S., Gusfield, D.: Untangling tanglegrams: Comparing trees by their drawings. Technical Report CSE-2009-1, UC Davis, Computer Science Department (2009)

    Google Scholar 

  29. Wan Zainon, W.N., Calder, P.: Visualising phylogenetic trees. In: Piekarski, W. (ed.) Seventh Australasian User Interface Conference (AUIC 2006), Hobart, Australia. CRPIT, vol. 50, pp. 145–152. ACS (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, UC Davis, USA

    Balaji Venkatachalam, Jim Apple & Dan Gusfield

  2. Department of Mathematics and Computer Science, Lehman College, and the Graduate Center, City University of New York, USA

    Katherine St. John

Authors
  1. Balaji Venkatachalam
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  2. Jim Apple
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  3. Katherine St. John
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  4. Dan Gusfield
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Editor information

Editors and Affiliations

  1. Computer Science & Engineering Department, University of Connecticut, 371 Fairfield Way, Unit 2155, CT 06269, Storrs, USA

    Ion Măndoiu

  2. Bioinformatics Research Group (BioRG), School of Computing and Information Sciences, Florida International University, 11200 SW 8th Street, Room ECS254, University Park, FL 33199, Miami, USA

    Giri Narasimhan

  3. Department of Computer Science, Georgia State University, P.O. Box 3994, GA 30302-3994, Atlanta, USA

    Yanqing Zhang

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Venkatachalam, B., Apple, J., St. John, K., Gusfield, D. (2009). Untangling Tanglegrams: Comparing Trees by Their Drawings. In: Măndoiu, I., Narasimhan, G., Zhang, Y. (eds) Bioinformatics Research and Applications. ISBRA 2009. Lecture Notes in Computer Science(), vol 5542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01551-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-01551-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01550-2

  • Online ISBN: 978-3-642-01551-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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