On a Fixed Haplotype Variant of the Minimum Error Correction Problem
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Haplotype assembly is the problem of reconstructing the two parental chromosomes of an individual from a set of sampled DNA-sequences. A combinatorial optimization problem that models haplotype assembly is the Minimum Error Correction problem (MEC). This problem has been intensively studied in the computational biology literature and is also known in the clustering literature: essentially we are required to find two cluster centres such that the sum of distances to the nearest centre, is minimized. We introduce here the problem Fixed haplotype-Minimum Error Correction (FH-MEC), a new variant of MEC which corresponds to instances where one of the haplotypes/centres is already given. We provide hardness results for the problem on various restricted instances. We also propose a new and very simple 2-approximation algorithm for MEC on binary input matrices.
The last author acknowledges the support of an NWO TOP 2 grant.