### Abstract

Background: Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome's copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. Results: We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile a to b by the minimum number of events needed to transform a into b. Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. Conclusions: For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. Availability:https://github.com/raphael-group/CNT-ILP.

Original language | English (US) |
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Article number | 13 |

Journal | Algorithms for Molecular Biology |

Volume | 12 |

Issue number | 1 |

DOIs | |

State | Published - May 16 2017 |

### All Science Journal Classification (ASJC) codes

- Structural Biology
- Molecular Biology
- Computational Theory and Mathematics
- Applied Mathematics

### Keywords

- Cancer
- Copy-number variant
- Maximum parsimony
- Phylogeny
- Somatic mutation

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## Cite this

*Algorithms for Molecular Biology*,

*12*(1), [13]. https://doi.org/10.1186/s13015-017-0103-2