, Volume 49, Issue 1, pp 13–36 | Cite as

The Complexity of the Single Individual SNP Haplotyping Problem

  • Rudi CilibrasiEmail author
  • Leo van IerselEmail author
  • Steven KelkEmail author
  • John TrompEmail author


We present several new results pertaining to haplotyping. These results concern the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype fragments. We consider the complexity of the problems Minimum Error Correction (MEC) and Longest Haplotype Reconstruction (LHR) for different restrictions on the input data. Specifically, we look at the gapless case, where every row of the input corresponds to a gapless haplotype-fragment, and the 1-gap case, where at most one gap per fragment is allowed. We prove that MEC is APX-hard in the 1-gap case and still NP-hard in the gapless case. In addition, we question earlier claims that MEC is NP-hard even when the input matrix is restricted to being completely binary. Concerning LHR, we show that this problem is NP-hard and APX-hard in the 1-gap case (and thus also in the general case), but is polynomial time solvable in the gapless case.


Polynomial Time Bipartite Graph Vertex Cover Input Matrix Directed Circuit 
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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Centrum voor Wiskunde en Informatica (CWI), Kruislaan 4131098 SJ AmsterdamThe Netherlands
  2. 2.Technische Universiteit Eindhoven, Den Dolech 25612 AX EindhovenThe Netherlands

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