On the Approximability of Some Haplotyping Problems

Authors:
John Abraham;Zhixiang Chen;Richard Fowler;Bin Fu;Binhai Zhu
Affiliations:
Department of Computer Science, University of Texas-American, Edinburg, USA TX 78739-2999;Department of Computer Science, University of Texas-American, Edinburg, USA TX 78739-2999;Department of Computer Science, University of Texas-American, Edinburg, USA TX 78739-2999;Department of Computer Science, University of Texas-American, Edinburg, USA TX 78739-2999;Department of Computer Science, Montana State University, Bozeman, USA MT 59717-3880
Venue:
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Year:
2009

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Abstract

In this paper, we study several versions of optimization problems related to haplotype reconstruction/identification. The input to the first problem is a set C 1 of haplotypes, a set C 2 of haplotypes, and a set G of genotypes. The objective is to select the minimum number of haplotypes from C 2 so that together with haplotypes in C 1 they resolve all (or the maximum number of) genotypes in G . We show that this problem has a factor-O (logn ) polynomial time approximation. We also show that this problem does not admit any approximation with a factor better than O (logn ) unless P=NP. For the corresponding reconstruction problem, i.e., when C 2 is not given, the same approximability results hold. The other versions of the haplotype identification problem are based on single individual haplotyping, including the well-known Minimum Fragment Removal (MFR) and Minimum SNP Removal (MSR), which have both shown to be APX-hard previously. We show in this paper that MFR has a polynomial time O (logn )-factor approximation. We also consider Maximum Fragment Identification (MFI), which is the complementary version of MFR; and Maximum SNP Identification (MSI), which is the complementary version of MSR. We show that, for any positive constant *** n 1 *** *** polynomial time approximation algorithm unless P=NP.