The pure parsimony haplotyping problem: overview and computational advances

Abstract

Haplotyping estimation from aligned single-nucleotide polymorphism fragments has attracted more and more attention in recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics, and pharmacogenetics. The literature proposes a number of estimation criteria to select a set of haplotypes among possible alternatives. Usually, such criteria can be expressed under the form of objective functions, and the sets of haplotypes that optimize them are referred to as optimal. One of the most important estimation criteria is the pure parsimony, which states that the optimal set of haplotypes for a given set of genotypes is that having minimal cardinality. Finding the minimal number of haplotypes necessary to explain a given set of genotypes involves solving an optimization problem, called the pure parsimony haplotyping ( PPH) estimation problem, which is notoriously NP-hard. This article provides an overview of PPH, and discusses the different approaches to solution that occur in the literature.

Extended Islands of Tractability for Parsimony Haplotyping

“…Over the last few years, haplotype inference has become one of the central problems in algorithmic bioinformatics [10,2]. Its applications include drug design, pharmacogenetics, mapping of disease genes, and inference of population histories.…”

“…One of the major approaches to haplotype inference is parsimony haplotyping: Given a set of genotypes, the task is to find a minimum-cardinality set of haplotypes that explains the input set of genotypes. The task to select as few haplotypes as possible (parsimony criterion) is motivated by the observation that in natural populations the number of haplotypes is much smaller than the number of genotypes [2]. Referring for the background in molecular biology to the rich literature (see, e.g., the surveys by Catanzaro and Labbé [2] and Gusfield and Orzack [10]), we focus on the underlying combinatorial problem.…”

“…The task to select as few haplotypes as possible (parsimony criterion) is motivated by the observation that in natural populations the number of haplotypes is much smaller than the number of genotypes [2]. Referring for the background in molecular biology to the rich literature (see, e.g., the surveys by Catanzaro and Labbé [2] and Gusfield and Orzack [10]), we focus on the underlying combinatorial problem. In an abstract way, a genotype can be seen as a length-m string over the alphabet {0, 1, 2}, while a haplotype can be seen as a length-m string over the alphabet {0, 1}.…”

“…Parsimony haplotyping is NP-hard, and numerous algorithmic approaches based on heuristics and integer linear programming methods are applied in practice [2]. There is also a growing list of combinatorial approaches (with provable performance guarantees) including the identification of polynomial-time solvable special cases, approximation algorithms, and fixed-parameter algorithms [5,13,14,16,11].…”

Effective heuristics for the Set Covering with Pairs Problem

“…In this approach the solution is built iteratively and, in each iteration, Some recent problems in computational biology can be treated as SCPP. The Pure Parsimony Haplotyping Problem (PPHP) is a problem where the objective is to determine a set of pairs of haplotypes H such that each genotype of a given set of genotypes G is resolved with a pair from H. This problem can be treated as a SCPP and some exact and non-exact algorithms were developed for solving it (Catanzaro and Labbé, 2009). Another biochemical problem that can be modeled as SCPP is the Polymerase Chain Reaction (PCR) Primer Design.…”