A Branch and Bound for the Large Live Parsimony Problem

Rogério Güths, Guilherme P. Telles, Maria Emilia M. T. Walter, Nalvo Almeida

Abstract

In the character-based phylogeny reconstruction for n objects and m characters, the input is an nm-matrix such that position i; j keeps the state of character j for the object i and the output is a binary rooted tree, where the input objects are represented as leaves and each node v is labeled with a string of m symbols v1 : : :vm, v j representing the state of character j, with minimal number of state changes along the edges of the tree, considering all characters. This is called the Large Parsimony Problem. Live Phylogeny theory generalizes the phylogeny theory by admitting living ancestors among the taxonomic objects. This theory suits cases of fast-evolving species like virus, and phylogenies of non-biological objects like documents, images and database records. In this paper we analyze problems related to most parsimonious tree using Live Phylogeny. We introduce the Large Live Parsimony Problem (LLPP), prove that it is NP-complete and provide a branch and bound solution. We also introduce and solve a simpler version, Small Live Parsimony Problem (SLPP), which is used in the branch and bound.

References

  1. Castro-Nallar, E., Perez-Losada, M., Burton, G., and Crandall, K. (2012). The evolution of HIV: Inferences using phylogenetics. Mol. Phylog. Evol., 62:777-792.
  2. Cuadros, A., Paulovich, F., Minghim, R., and Telles, G. (2007). Point placement by phylogenetic trees and its application to visual analysis of document collections. In Proc. of the 2007 IEEE Symposium on Visual Analytics Science and Technology, pages 99-106.
  3. Felsenstein, J. (2004). Inferring Phylogenies. Sinauer As.
  4. Fitch, W. (1971). Toward defining the course of evolution: Minimum change for a specific tree topology. Systematic Zoology, 20:406-416.
  5. Goëffon, A., Richer, J., and Hao, J. (2011). Heuristic Methods for Phylogenetic Reconstruction with Maximum Parsimony, pages 579-597. John Wiley & Sons, Inc.
  6. Gojobori, T., Moriyama, E., and Kimura, M. (1990). Molecular clock of viral evolution, and the neutral theory. P. Natl. Acad. Sci., 87(24):10015-10018.
  7. Hendy, M. and Penny, D. (1982). Branch and bound algorithms to determine minimal evolutionary trees. Mathematical Biosciences, 59(2):277 - 290.
  8. Jones, N. C. and Pevzner, P. A. (2004). An Introduction to Bioinformatics Algorithms, volume 2004. MIT Press.
  9. Paiva, J., Florian, L., Pedrini, H., Telles, G., and Minghim, R. (2011). Improved similarity trees and their application to visual data classification. IEEE Trans. Vis. Comp. Graphics, 17(12):2459-2468.
  10. Sankoff, D. (1975). Minimal mutation trees of sequences. SIAM Journal of Applied Mathematics, 28(1):35-42.
  11. Setubal, J. and Meidanis, J. (1997). Introduction to Molecular Computational Biology, volume 1997. PWS.
  12. Telles, G., Almeida, N., Minghim, R., and Walter, M. (2013). Live phylogeny. Journal of Computational Biology, 20(1):30-37.
  13. Yan, M. and Bader, D. A. (2003). Fast character optimization in parsimony phylogeny reconstruction. Tec. Report TR-CS-2003-53, Univ. of New Mexico.
Download


Paper Citation


in Harvard Style

Güths R., Telles G., Walter M. and Almeida N. (2017). A Branch and Bound for the Large Live Parsimony Problem . In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017) ISBN 978-989-758-214-1, pages 184-189. DOI: 10.5220/0006219001840189


in Bibtex Style

@conference{bioinformatics17,
author={Rogério Güths and Guilherme P. Telles and Maria Emilia M. T. Walter and Nalvo Almeida},
title={A Branch and Bound for the Large Live Parsimony Problem},
booktitle={Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017)},
year={2017},
pages={184-189},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006219001840189},
isbn={978-989-758-214-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017)
TI - A Branch and Bound for the Large Live Parsimony Problem
SN - 978-989-758-214-1
AU - Güths R.
AU - Telles G.
AU - Walter M.
AU - Almeida N.
PY - 2017
SP - 184
EP - 189
DO - 10.5220/0006219001840189