Extended Islands of Tractability for Parsimony Haplotyping

Parsimony haplotyping is the problem of finding a smallest size set of haplotypes that can explain a given set of genotypes. The problem is NP-hard, and many heuristic and approximation algorithms as well as polynomial-time solvable special cases have been discovered. We propose improved fixed-parameter tractability results with respect to the parameter "size of the target haplotype set" k by presenting an O*(k4k)-time algorithm. This also applies to the practically important constrained case, where we can only use haplotypes from a given set. Furthermore, we show that the problem becomes polynomial-time solvable if the given set of genotypes is complete, i.e., contains all possible genotypes that can be explained by the set of haplotypes.

[1]  Rolf Niedermeier,et al.  Invitation to Fixed-Parameter Algorithms , 2006 .

[2]  Martine Labbé,et al.  The pure parsimony haplotyping problem: overview and computational advances , 2009, Int. Trans. Oper. Res..

[3]  Michael A. Langston,et al.  Parameterized and Exact Computation, Second International Workshop, IWPEC 2006, Zürich, Switzerland, September 13-15, 2006, Proceedings , 2006, IWPEC.

[4]  Giuseppe Lancia,et al.  Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms , 2004, INFORMS J. Comput..

[5]  Jörg Flum,et al.  Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[6]  L. van lersel,et al.  Shorelines of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems , 2008, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[7]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[8]  Michael R. Fellows,et al.  On problems without polynomial kernels , 2009, J. Comput. Syst. Sci..

[9]  Gad M. Landau,et al.  Haplotype Inference Constrained by Plausible Haplotype Data , 2009, CPM.

[10]  Roded Sharan,et al.  Islands of Tractability for Parsimony Haplotyping , 2005, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[11]  Weixiong Zhang,et al.  Complete Parsimony Haplotype Inference Problem and Algorithms , 2009, ESA.

[12]  Rolf Niedermeier,et al.  A Structural View on Parameterizing Problems: Distance from Triviality , 2004, IWPEC.

[13]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[14]  Ferdinando Cicalese,et al.  On Parsimony Haplotyping , 2008 .

[15]  Amos Fiat,et al.  Algorithms - ESA 2009 , 2009, Lecture Notes in Computer Science.

[16]  Xin Li,et al.  Haplotype inference. , 2012, Methods in molecular biology.

[17]  Rolf Niedermeier,et al.  Invitation to data reduction and problem kernelization , 2007, SIGA.

[18]  Lance Fortnow,et al.  Infeasibility of instance compression and succinct PCPs for NP , 2007, J. Comput. Syst. Sci..

[19]  Giuseppe Lancia,et al.  A polynomial case of the parsimony haplotyping problem , 2006, Oper. Res. Lett..