Construction of random perfect phylogeny matrix

Abstract

Mehdi Sadeghi1,2, Hamid Pezeshk4, Changiz Eslahchi3,5, Sara Ahmadian6, Sepideh Mah Abadi61National Institute of Genetic Engineering and Biotechnology, Tehran, Iran; 2School of Computer Science, 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran; 4School of Mathematics, Statistics and Computer Sciences, Center of Excellence in Biomathematics, College of Science, University of Tehran, Tehran, Iran; 5Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran; 6Department of Computer Engineering, Sharif University of Technology, Tehran, IranPurpose: Interest in developing methods appropriate for mapping increasing amounts of genome-wide molecular data are increasing rapidly. There is also an increasing need for methods that are able to efficiently simulate such data.Patients and methods: In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs), and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b.Results: We introduce an O(max(n2, nm)) algorithm for the random construction of such a phylogeny matrix. The running time of any algorithm for solving this problem would be Ω (nm).Conclusion: We have developed software, RAPPER, based on this algorithm, which is available at http://bioinf.cs.ipm.ir/softwares/RAPPER.Keywords: perfect phylogeny, minimum allele frequency (MAF), tree, recursive algorithm