# The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification

Hans-Joachim Böckenhauer; Michal Forišek; Ján Oravec; Björn Steffen; Kathleen Steinhöfel; Monika Steinová

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 44, Issue: 3, page 363-377
- ISSN: 0988-3754

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topBöckenhauer, Hans-Joachim, et al. "The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification." RAIRO - Theoretical Informatics and Applications 44.3 (2010): 363-377. <http://eudml.org/doc/250809>.

@article{Böckenhauer2010,

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.
},

author = {Böckenhauer, Hans-Joachim, Forišek, Michal, Oravec, Ján, Steffen, Björn, Steinhöfel, Kathleen, Steinová, Monika},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Exact algorithms; fixed-parameter algorithms; minimum-ones 2SAT; haplotypes; exact algorithms},

language = {eng},

month = {10},

number = {3},

pages = {363-377},

publisher = {EDP Sciences},

title = {The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification},

url = {http://eudml.org/doc/250809},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Böckenhauer, Hans-Joachim

AU - Forišek, Michal

AU - Oravec, Ján

AU - Steffen, Björn

AU - Steinhöfel, Kathleen

AU - Steinová, Monika

TI - The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/10//

PB - EDP Sciences

VL - 44

IS - 3

SP - 363

EP - 377

AB -
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.

LA - eng

KW - Exact algorithms; fixed-parameter algorithms; minimum-ones 2SAT; haplotypes; exact algorithms

UR - http://eudml.org/doc/250809

ER -

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