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The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification
Published online by Cambridge University Press: 28 July 2010
Abstract
Analyzing genomic data for finding those gene variations which are
responsible for hereditary diseases is one of the great challenges in
modern bioinformatics. In many living beings (including the human), every
gene is present in two copies, inherited from the two parents, the
so-called haplotypes. In this paper, we propose a simple
combinatorial model for classifying the set of haplotypes in a population
according to their responsibility for a certain genetic disease. This
model is based on the minimum-ones 2SAT problem with uniform clauses.
The minimum-ones 2SAT problem asks for a satisfying assignment to
a satisfiable formula in 2CNF which sets a minimum number of variables to
true. This problem is well-known to be $\mathcal{NP}$-hard, even in the
case where all clauses are uniform, i.e., do not contain a positive and
a negative literal. We analyze the approximability and present the first
non-trivial exact algorithm for the uniform minimum-ones 2SAT problem
with a running time of $\mathcal{O}$
(1.21061n)
on a 2SAT formula with n variables.
We also show that the problem is fixed-parameter tractable by showing
that our algorithm can be adapted to verify in $\mathcal{O}^*$
(2k) time
whether an assignment with at most k true variables exists.
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- Research Article
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- Copyright
- © EDP Sciences, 2010
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