On the Complexity of Several Haplotyping Problems ## AbstractWe present several new results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More specifically, we show that an interesting, restricted case of \emph{Minimum Error Correction} (MEC) is NP-hard, question earlier claims about a related problem, and present a polynomial-time algorithm for the ungapped case of \emph{Longest Haplotype Reconstruction} (LHR). Secondly, wepresent a polynomial time algorithm for the problem of resolving genotype data using as few haplotypes as possible (the \emph{Pure Parsimony Haplotyping Problem}, PPH) where each genotype has at most two ambiguous positions, thus solving an open problem posed by Lancia et al in \cite{pureparsimony}.
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