Skip to main content
Log in

Maximal sub-triangulation in pre-processing phylogenetic data

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In order to help infer an evolutionary tree (phylogeny) from experimental data, we propose a new method for pre-processing the corresponding dissimilarity matrix, which is related to the property that the distance matrix of a phylogeny (called an additive matrix) describes a sandwich family of chordal graphs. As experimental data often yield distance values which are known to be under-estimated, we address the issue of correcting the data by increasing the distances which are incorrect. This is done by computing, for each graph of the sandwich family, a maximal chordal subgraph.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Balas E (1986) A fast algorithm for finding an edge-maximal subgraph with a TR-formative coloring. Discrete Appl Math 15:123–134

    Google Scholar 

  2. Barthélémy J-P, Guénoche A (1991) Trees and proximity representations. Wiley (eds), New York

  3. Berry A (1999) A wide-range efficient algorithm for minimal triangulation. In: Proceedings of tenth annual ACM-SIAM symposium on discrete algorithms (SODA'99), 860–861

  4. Berry A, Blair J, Heggernes P (2002) Maximum cardinality search for computing minimal triangulations. In: Kucera L (ed) Graph theoretical concepts in computer science – WG 2002, LNCS 2573, Springer Berlin Heidelberg New York 1–12

  5. Berry A, Bordat J-P, Heggernes P (2000) Recognizing weakly triangulated graphs by edge separability. Nordic J Comput 7:164–177

    Google Scholar 

  6. Berry A, Heggernes P, Villanger Y (2003) An on-line incremental approach for dynamically maintaining chordal graphs. Research Report LIMOS: RR 2003-04

  7. Berry A, Bordat J-P, Heggernes P, Simonet G, Villanger Y (2003) A wide-range algorithm for minimal triangulation from an arbitrary ordering. Technical report reports in informatics 243, University of Bergen (Norway); Research Report LIMOS: RR 2003-02. J Algorithms (submitted)

  8. Berry A, Sigayret A, Sinoquet C (2002) Towards improving phylogeny reconstruction with combinatorial-based constraints on an underlying family of graphs. Research Report LIMOS: RR 02-103

  9. Berry V, Gascuel O (2000) Inferring evolutionary trees with strong combinatorial evidence. Theor Comput Sci 240 2:271–298

    Google Scholar 

  10. Blair JRS, Peyton B (1993) An introduction to chordal graphs and clique trees. Graph Theory Sparse Matrix Comput 56:1–29

  11. Bonnot F, Guénoche A, Perrier X (1996) Properties of an order distance associated with a tree distance. In: Diday E et al (eds) Proceedings of OSDA'95 (Ordinal and Symbolic Data Analysis), Springer Berlin Heidelberg New York 252–261

  12. Brandstädt A, Le VB, Spinrad J (1999) Graph classes – a survey. SIAM monographs on discrete mathematics and applications

  13. Buneman P (1971) The recovery of trees from measures of dissimilarity. Mathematics in the archeological and historical sciences. Edinburgh University Press, 387–395

  14. Buneman P (1974) A characterization of rigid circuit graphs. Discrete Math 9:205–212

    Google Scholar 

  15. Coleman TF (1988) A chordal preconditioner for large-scale optimization. Appl Math 40:265–287

    Google Scholar 

  16. Dearing PM, Shier DR, Warner DD (1988) Maximal chordal subgraphs. Discrete Appl Math 20:181–190

    Google Scholar 

  17. Erdös P, Laskar R (1983) On maximum chordal subgraph. Cong Numerantium 39:367–373

    Google Scholar 

  18. Garetta H, Guénoche A (2001) How confident can we be that a tree representation is good? (Quelle confiance accorder à une représentation arborée?). In: Gascuel O, Sagot M-F (eds) Proceedings of JOBIM 2000, LNCS, vol 2066 Springer Berlin Heidelberg, New York pp 45–56

  19. Gàvril F (1974) The intersection graphs of subtrees of trees are exactly the chordal graphs. J Comb Theory B, 16:47–56

    Google Scholar 

  20. Golumbic MC (1980) Algorithmic graph theory and perfect graphs. Academic Press New York

  21. Guénoche A (1998) Ordinal properties of tree distances. Discrete Appl Math 192:103–117

    Google Scholar 

  22. Hayward R, Hoàng C, Maffray F (1989) Optimizing weakly triangulated graphs. Graphs Comb 5:339–349

    Google Scholar 

  23. Hein J (1989) An optimal algorithm to reconstruct trees from additive distance data. Bull Math Biol 51(5):597–603

    Google Scholar 

  24. Huson D, Nettles S, Warnow T (1999) Obtaining highly accurate topology estimates of evolutionary trees from very short sequences. In: Proceedings of RECOMB'99, Lyon (France), 198–207

  25. Ibarra L (2000) Fully dynamic algorithms for chordal graphs and split graphs. Technical report, University of Victoria DCS-262-IR

  26. Kearney P, Hayward R, Meijer H (1997) Inferring evolutionary trees from ordinal data. In: Proceedings of eighth annual ACM-SIAM symposium on Discrete Algorithms (SODA'97) 418–426

  27. Rose D, Tarjan RE, Lueker G (1976) Algorithmic aspects of vertex elimination on graphs. SIAM J Comput 5:146–160

    Google Scholar 

  28. Spinrad J, Sritharan R (1995) Algorithms for weakly triangulated graphs. Discrete Appl Math 59:181–191

    Google Scholar 

  29. Walter JR (1978) Representations of Chordal Graphs as Subtrees of a Tree. J Graph Theory 2:265–267

    Google Scholar 

  30. Xue J (1994) Edge-maximal triangulated subgraphs and heuristics for the maximum clique problem. Networks 24:109–120

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anne Berry.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berry, A., Sigayret, A. & Sinoquet, C. Maximal sub-triangulation in pre-processing phylogenetic data. Soft Comput 10, 461–468 (2006). https://doi.org/10.1007/s00500-005-0507-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-005-0507-7

Keywords

Navigation