Skip to main content
SpringerLink
Log in

Incomplete Directed Perfect Phylogeny in Linear Time

  • Conference paper
  • First Online:
Algorithms and Data Structures (WADS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12808))

Included in the following conference series:

  • 1062 Accesses

Abstract

Reconstructing the evolutionary history of a set of species is a central task in computational biology. In real data, it is often the case that some information is missing: the Incomplete Directed Perfect Phylogeny (IDPP) problem asks, given a collection of species described by a set of binary characters with some unknown states, to complete the missing states in such a way that the result can be explained with a directed perfect phylogeny. Pe’er et al. [SICOMP 2004] proposed a solution that takes \(\tilde{\mathcal {O}}(nm)\) time (the \(\tilde{\mathcal {O}}(\cdot )\) notation suppresses polylog factors) for n species and m characters. Their algorithm relies on pre-existing dynamic connectivity data structures: a computational study recently conducted by Fernández-Baca and Liu showed that, in this context, complex data structures perform worse than simpler ones with worse asymptotic bounds.

This gives us the motivation to look into the particular properties of the dynamic connectivity problem in this setting, so as to avoid the use of sophisticated data structures as a blackbox. Not only are we successful in doing so, and give a much simpler \(\mathcal {O}(nm\log n)\)-time algorithm for the IDPP problem; our insights into the specific structure of the problem lead to an asymptotically optimal \(\mathcal {O}(nm)\)-time algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The \(\tilde{\mathcal {O}}(\cdot )\) notation suppresses polylog factors.

References

  1. Bashir, A., Ye, C., Price, A.L., Bafna, V.: Orthologous repeats and mammalian phylogenetic inference. Genome Res. 15(7), 998–1006 (2005)

    Article  Google Scholar 

  2. Bodlaender, H.L., Fellows, M.R., Hallett, M.T., Wareham, H.T., Warnow, T.J.: The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs. Theoret. Comput. Sci. 244(1–2), 167–188 (2000)

    Article  MathSciNet  Google Scholar 

  3. Bonizzoni, P., Braghin, C., Dondi, R., Trucco, G.: The binary perfect phylogeny with persistent characters. Theoret. Comput. Sci. 454, 51–63 (2012)

    Article  MathSciNet  Google Scholar 

  4. Bonizzoni, P., Ciccolella, S., Della Vedova, G., Soto, M.: Beyond perfect phylogeny: Multisample phylogeny reconstruction via ilp. In: 8th ACM-BCB, pp. 1–10 (2017)

    Google Scholar 

  5. Camin, J.H., Sokal, R.R.: A method for deducing branching sequences in phylogeny. Evolution, pp. 311–326 (1965)

    Google Scholar 

  6. El-Kebir, M.: Sphyr: tumor phylogeny estimation from single-cell sequencing data under loss and error. Bioinformatics 34(17), i671–i679 (2018)

    Article  Google Scholar 

  7. Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification-a technique for speeding up dynamic graph algorithms. J. ACM 44(5), 669–696 (1997)

    Article  MathSciNet  Google Scholar 

  8. Even, S., Shiloach, Y.: An on-line edge-deletion problem. J. ACM 28(1), 1–4 (1981)

    Article  MathSciNet  Google Scholar 

  9. Fernández-Baca, D., Liu, L.: Tree compatibility, incomplete directed perfect phylogeny, and dynamic graph connectivity: An experimental study. Algorithms 12(3), 53 (2019)

    Article  MathSciNet  Google Scholar 

  10. Gibb, D., Kapron, B., King, V., Thorn, N.: Dynamic graph connectivity with improved worst case update time and sublinear space. arXiv:1509.06464 (2015)

  11. Gusfield, D.: Efficient algorithms for inferring evolutionary trees. Networks 21(1), 19–28 (1991)

    Article  MathSciNet  Google Scholar 

  12. Gusfield, D.: Persistent phylogeny: a galled-tree and integer linear programming approach. In: 6th ACM-BCB, pp. 443–451 (2015)

    Google Scholar 

  13. Halperin, E., Karp, R.M.: Perfect phylogeny and haplotype assignment. In: Proceedings of the Eighth Annual International Conference on Resaerch in Computational Molecular Biology, pp. 10–19 (2004)

    Google Scholar 

  14. Henzinger, M.R., King, V., Warnow, T.: Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica 24(1), 1–13 (1999)

    Article  MathSciNet  Google Scholar 

  15. Holm, J., De Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM 48(4), 723–760 (2001)

    Article  MathSciNet  Google Scholar 

  16. Huang, S.E., Huang, D., Kopelowitz, T., Pettie, S.: Fully dynamic connectivity in \(O(\log n(\log \log n)^2)\) amortized expected time. In: 28th SODA, pp. 510–520. SIAM (2017)

    Google Scholar 

  17. Kimmel, G., Shamir, R.: The incomplete perfect phylogeny haplotype problem. J. Bioinform. Comput. Biol. 3(02), 359–384 (2005)

    Article  Google Scholar 

  18. Kirkpatrick, B., Stevens, K.: Perfect phylogeny problems with missing values. IEEE/ACM Trans. Comput. Biol. Bioinf. 11(5), 928–941 (2014)

    Article  Google Scholar 

  19. Nikaido, M., Rooney, A.P., Okada, N.: Phylogenetic relationships among cetartiodactyls based on insertions of short and long interpersed elements: hippopotamuses are the closest extant relatives of whales. Proc. Natl. Acad. Sci. 96(18), 10261–10266 (1999)

    Article  Google Scholar 

  20. Pe’er, I., Pupko, T., Shamir, R., Sharan, R.: Incomplete directed perfect phylogeny. SIAM J. Comput. 33(3), 590–607 (2004)

    Article  MathSciNet  Google Scholar 

  21. Satas, G., Zaccaria, S., Mon, G., Raphael, B.J.: Scarlet: Single-cell tumor phylogeny inference with copy-number constrained mutation losses. Cell Syst. 10(4), 323–332 (2020)

    Article  Google Scholar 

  22. Satya, R.V., Mukherjee, A.: The undirected incomplete perfect phylogeny problem. IEEE/ACM Trans. Comput. Biol. Bioinf. 5(4), 618–629 (2008)

    Article  Google Scholar 

  23. Shiloach, Y., Vishkin, U.: An \(o(\log n)\) parallel connectivity algorithm. J. Algorithms 3(1), 57–67 (1982)

    Article  MathSciNet  Google Scholar 

  24. Stevens, K., Gusfield, D.: Reducing multi-state to binary perfect phylogeny with applications to missing, removable, inserted, and deleted data. In: Moulton, V., Singh, M. (eds.) Algorithms in Bioinformatics. WABI 2010. Lecture Notes in Computer Science, vol. 6293. Springer, Berlin, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15294-8_23

  25. Thorup, M.: Decremental dynamic connectivity. J. Algorithms 33(2), 229–243 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 872539. GB was supported by the Netherlands Organisation for Scientific Research (NWO) under project OCENW.GROOT.2019.015 “Optimization for and with Machine Learning (OPTIMAL)”.

Author information

Authors and Affiliations

  1. Università degli Studi di Milano - Bicocca, Milano, Italy

    Giulia Bernardini & Paola Bonizzoni

  2. Institute of Computer Science, University of Wrocław, Wrocław, Poland

    Paweł Gawrychowski

  3. CWI, Amsterdam, The Netherlands

    Giulia Bernardini

Authors
  1. Giulia Bernardini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paola Bonizzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paweł Gawrychowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giulia Bernardini .

Editor information

Editors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Anna Lubiw

  2. University of Alberta, Edmonton, AB, Canada

    Mohammad Salavatipour

  3. Dalhousie University, Halifax, Canada

    Meng He

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bernardini, G., Bonizzoni, P., Gawrychowski, P. (2021). Incomplete Directed Perfect Phylogeny in Linear Time. In: Lubiw, A., Salavatipour, M., He, M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science(), vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-83508-8_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-83507-1

  • Online ISBN: 978-3-030-83508-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation