# 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

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#### 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