Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
A parsimonious tree-grow method for haplotype inference
Bioinformatics
Haplotype Phasing Using Semidefinite Programming
BIBE '05 Proceedings of the Fifth IEEE Symposium on Bioinformatics and Bioengineering
Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms
INFORMS Journal on Computing
Haplotype inference by pure Parsimony
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Boosting Haplotype Inference with Local Search
Constraints
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Two-Level ACO for Haplotype Inference Under Pure Parsimony
ANTS '08 Proceedings of the 6th international conference on Ant Colony Optimization and Swarm Intelligence
A Set-Covering Approach with Column Generation for Parsimony Haplotyping
INFORMS Journal on Computing
Pure Parsimony Xor Haplotyping
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
A Decomposition of the Pure Parsimony Haplotyping Problem
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
HAPLO-ASP: Haplotype Inference Using Answer Set Programming
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Efficient haplotype inference with answer set programming
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
A new preprocessing procedure for the haplotype inference problem
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Efficient haplotype inference with pseudo-boolean optimization
AB'07 Proceedings of the 2nd international conference on Algebraic biology
EPIA'07 Proceedings of the aritficial intelligence 13th Portuguese conference on Progress in artificial intelligence
Efficient haplotype inference with combined CP and OR techniques
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A Class Representative Model for Pure Parsimony Haplotyping
INFORMS Journal on Computing
Constructing majority-rule supertrees
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
CollHaps: A Heuristic Approach to Haplotype Inference by Parsimony
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
SplittingHeirs: inferring haplotypes by optimizing resultant dense graphs
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Phylogeny - and parsimony-based haplotype inference with constraints
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Pure Parsimony Xor Haplotyping
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Phylogeny- and parsimony-based haplotype inference with constraints
Information and Computation
SAT in bioinformatics: making the case with haplotype inference
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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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 polynomial-sized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomial-sized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomial-sized 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 exponential-sized 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.