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31
Integer programming approaches to haplotype inference by pure parsimony
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
, 2006
"... Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case ..."
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Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case. Several authors [2], [3] have presented polynomialsized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomialsized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomialsized IP formulation that is a hybrid between two existing IP formulations and inherits many of the strengths of both. Many problems that are too complex for the exponentialsized formulations can still be solved in our new formulation in a reasonable amount of time. We provide a detailed empirical comparison of these IP formulations on both simulated and real genotype sequences. Our formulation can also be extended in a variety of ways to allow errors in the input or model the structure of the population under consideration. Index Terms—Computations on discrete structures, integer programming, biology and genetics, haplotype inference. 1
Islands of Tractability for Parsimony Haplotyping
 Proc. IEEE Computational Systems Bioinformatics Conf
, 2005
"... We study the parsimony approach to haplotype inference, which calls for finding a set of haplotypes of minimum cardinality that explains an input set of genotypes. We prove that the problem is APXhard even in very restricted cases. On the positive side, we identify islands of tractability for the p ..."
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Cited by 13 (2 self)
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We study the parsimony approach to haplotype inference, which calls for finding a set of haplotypes of minimum cardinality that explains an input set of genotypes. We prove that the problem is APXhard even in very restricted cases. On the positive side, we identify islands of tractability for the problem, by focusing on instances with specific structure of haplotype sharing among the input genotypes. We exploit the structure of those instance to give polynomial and constantapproximation algorithms to the problem. We also show that the general parsimony haplotyping problem is fixed parameter tractable.
Boosting Haplotype Inference with Local Search
"... Abstract. A very challenging problem in the genetics domain is to infer haplotypes from genotypes. This process is expected to identify genes affecting health, disease and response to drugs. One of the approaches to haplotype inference aims to minimise the number of different haplotypes used, and is ..."
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Cited by 7 (2 self)
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Abstract. A very challenging problem in the genetics domain is to infer haplotypes from genotypes. This process is expected to identify genes affecting health, disease and response to drugs. One of the approaches to haplotype inference aims to minimise the number of different haplotypes used, and is known as haplotype inference by pure parsimony (HIPP). The HIPP problem is computationally difficult, being NPhard. Recently, a SATbased method (SHIPs) has been proposed to solve the HIPP problem. This method iteratively considers an increasing number of haplotypes, starting from an initial lower bound. Hence, one important aspect of SHIPs is the lower bounding procedure, which reduces the number of iterations of the basic algorithm, and also indirectly simplifies the resulting SAT model. This paper describes the use of local search to improve existing lower bounding procedures. The new lower bounding procedure is guaranteed to be as tight as the existing procedures. In practice the new procedure is in most cases considerably tighter, allowing significant improvement of performance on challenging problem instances. 1
Minimum multicolored subgraph problem in multiplex pcr primer set selection and population haplotyping
 In Proceedings of the 6th International Conference on Computational Science (ICCS
, 2006
"... Abstract. In this paper we consider the minimum weight multicolored subgraph problem (MWMCSP), which is a common generalization of minimum cost multiplex PCR primer set selection and maximum likelihood population haplotyping. In this problem one is given an undirected graph G with nonnegative verte ..."
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Abstract. In this paper we consider the minimum weight multicolored subgraph problem (MWMCSP), which is a common generalization of minimum cost multiplex PCR primer set selection and maximum likelihood population haplotyping. In this problem one is given an undirected graph G with nonnegative vertex weights and a color function that assigns to each edge one or more of n given colors, and the goal is to find a minimum weight set of vertices inducing edges of all n colors. We obtain improved approximation algorithms and hardness results for MWMCSP and its variant in which the goal is to find a minimum number of vertices inducing edges of at least k colors for a given integer k ≤ n. 1
The Minimum Substring Cover Problem
"... Abstract. In this paper we consider the problem of covering a set of strings S with a set C of substrings in S, where C is said to cover S if every string in S can be written as a concatenation of the substrings in C. We discuss applications for the problem that arise in the context of computational ..."
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Cited by 5 (2 self)
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Abstract. In this paper we consider the problem of covering a set of strings S with a set C of substrings in S, where C is said to cover S if every string in S can be written as a concatenation of the substrings in C. We discuss applications for the problem that arise in the context of computational biology and formal language theory. We then proceed to show that this problem is at least as hard as the Minimum Set Cover problem. In the main part of the paper, we focus on devising approximation algorithms for the problem using two generic paradigms – the localratio technique and linear programming rounding. 1
Stochastic local search for largescale instances of the Haplotype Inference Problem by Parsimony Abstract
"... Haplotype Inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This information allows researchers to perform association studies for the genetic variants involved in diseases and the indiv ..."
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Haplotype Inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This information allows researchers to perform association studies for the genetic variants involved in diseases and the individual responses to therapeutic agents. A notable approach to the problem is to encode it as a combinatorial problem (under certain hypotheses, such as the pure parsimony criterion) and to solve it using offtheshelf combinatorial optimization techniques. The main methods applied to Haplotype Inference are either simple greedy heuristic or exact methods (Integer Linear Programming, Semidefinite Programming, SAT and pseudoboolean encoding) that, at present, are adequate only for moderate size instances. In this paper, we present and discuss an approach based on the combination of local search metaheuristics and a reduction procedure based on an analysis of the problem structure. Some relevant design issues are first described, then a family of local search metaheuristics is defined to tackle the Haplotype Inference. Results on common Haplotype Inference benchmarks show that the approach achieves a good tradeoff between solution quality and execution time.
Efficient and Tight Upper Bounds for Haplotype Inference by Pure Parsimony using Delayed Haplotype Selection
"... Abstract. Haplotype inference from genotype data is a key step towards a better understanding of the role played by genetic variations on inherited diseases. One of the most promising approaches uses the pure parsimony criterion. This approach is called Haplotype Inference by Pure Parsimony (HIPP) a ..."
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Cited by 4 (2 self)
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Abstract. Haplotype inference from genotype data is a key step towards a better understanding of the role played by genetic variations on inherited diseases. One of the most promising approaches uses the pure parsimony criterion. This approach is called Haplotype Inference by Pure Parsimony (HIPP) and is NPhard as it aims at minimising the number of haplotypes required to explain a given set of genotypes. The HIPP problem is often solved using constraint satisfaction techniques, for which the upper bound on the number of required haplotypes is a key issue. Another very wellknown approach is Clark’s method, which resolves genotypes by greedily selecting an explaining pair of haplotypes. In this work, we combine the basic idea of Clark’s method with a more sophisticated method for the selection of explaining haplotypes, in order to explicitly introduce a bias towards parsimonious explanations. This new algorithm can be used either to obtain an approximated solution to the HIPP problem or to obtain an upper bound on the size of the pure parsimony solution. This upper bound can then used to efficiently encode the problem as a constraint satisfaction problem. The experimental evaluation, conducted using a large set of real and artificially generated examples, shows that the new method is much more effective than Clark’s method at obtaining parsimonious solutions, while keeping the advantages of simplicity and speed of Clark’s method. 1
Gaspero. Twolevel ACO for haplotype inference under pure parsimony
 In Ant Colony Optimization and Swarm Intelligence, 6th International Workshop, ANTS 2008, volume 5217 of Lecture Notes in Computer Science
, 2008
"... Abstract. Haplotype Inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This information enables researchers to perform association studies for the genetic variants involved in diseases an ..."
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Cited by 4 (2 self)
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Abstract. Haplotype Inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This information enables researchers to perform association studies for the genetic variants involved in diseases and the individual responses to therapeutic agents. A notable approach to the problem is to encode it as a combinatorial problem under certain hypotheses (such as the pure parsimony criterion) and to solve it using offtheshelf combinatorial optimization techniques. At present, the main methods applied to Haplotype Inference are either simple greedy heuristic or exact methods, which are adequate only for moderate size instances. In this paper, we present an iterative constructive approach to Haplotype Inference based on ACO and we compare it against a stateoftheart exact method. 1