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On the Approximability of Some Haplotyping Problems

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Algorithmic Aspects in Information and Management (AAIM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5564))

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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 ε< 1, neither MFI nor MSI has a factor-n 1 − ε polynomial time approximation algorithm unless P=NP.

This research is partially supported by NSF Career Award 0845376.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas-American, Edinburg, TX 78739-2999, USA

    John Abraham, Zhixiang Chen, Richard Fowler & Bin Fu

  2. Department of Computer Science, Montana State University, Bozeman, MT 59717-3880, USA

    Binhai Zhu

Authors
  1. John Abraham
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  2. Zhixiang Chen
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  3. Richard Fowler
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  4. Bin Fu
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  5. Binhai Zhu
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Editors and Affiliations

  1. Microsoft Research – Silicon Valley, 1065 La Avenida, Mountain View, CA 94062, USA

    Andrew V. Goldberg

  2. Rocket Fuel Inc., 350 Marine Parkway, CA 94065, Marina Park Center, USA

    Yunhong Zhou

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Abraham, J., Chen, Z., Fowler, R., Fu, B., Zhu, B. (2009). On the Approximability of Some Haplotyping Problems. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-02158-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02157-2

  • Online ISBN: 978-3-642-02158-9

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