WABI 2016: Algorithms in Bioinformatics pp 137-149

# Copy-Number Evolution Problems: Complexity and Algorithms

• Mohammed El-Kebir
• Benjamin J. Raphael
• Ron Shamir
• Roded Sharan
• Simone Zaccaria
• Meirav Zehavi
• Ron Zeira
Conference paper

DOI: 10.1007/978-3-319-43681-4_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9838)
Cite this paper as:
El-Kebir M. et al. (2016) Copy-Number Evolution Problems: Complexity and Algorithms. In: Frith M., Storm Pedersen C. (eds) Algorithms in Bioinformatics. WABI 2016. Lecture Notes in Computer Science, vol 9838. Springer, Cham

## Abstract

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 are 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. We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile $$\mathbf {a}$$ to $$\mathbf {b}$$ by the minimum number of events needed to transform $$\mathbf {a}$$ into $$\mathbf {b}$$. 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. 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. We assess the efficiency and quality of our algorithms on simulated instances.

© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Mohammed El-Kebir
• 1
• Benjamin J. Raphael
• 1
• Ron Shamir
• 2
• Roded Sharan
• 2
• Simone Zaccaria
• 1
• 3
• Meirav Zehavi
• 2
• Ron Zeira
• 2
1. 1.Department of Computer Science, Center for Computational Molecular BiologyBrown UniversityProvidenceUSA
2. 2.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
3. 3.Dipartimento di Informatica Sistemistica E Comunicazione (DISCo)Univ. Degli Studi di Milano-BicoccaMilanItaly