Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT
  and its Algorithmic Applications   A pair of unit clauses is called conflicting if it is of the form $(x)$,
$(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair
of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed
that for each UCF CNF formula with $m$ clauses we can simultaneously satisfy at
least $\pp m$ clauses, where $\pp =(\sqrt{5}-1)/2$. We improve the
Lieberherr-Specker bound by showing that for each UCF CNF formula $F$ with $m$
clauses we can find, in polynomial time, a subformula $F'$ with $m'$ clauses
such that we can simultaneously satisfy at least $\pp m+(1-\pp)m'+(2-3\pp)n"/2$
clauses (in $F$), where $n"$ is the number of variables in $F$ which are not in
$F'$.
  We consider two parameterized versions of MAX-SAT, where the parameter is the
number of satisfied clauses above the bounds $m/2$ and $m(\sqrt{5}-1)/2$. The
former bound is tight for general formulas, and the later is tight for UCF
formulas. Mahajan and Raman (J. Algorithms 31, 1999) showed that every instance
of the first parameterized problem can be transformed, in polynomial time, into
an equivalent one with at most $6k+3$ variables and $10k$ clauses. We improve
this to $4k$ variables and $(2\sqrt{5}+4)k$ clauses. Mahajan and Raman
conjectured that the second parameterized problem is fixed-parameter tractable
(FPT). We show that the problem is indeed FPT by describing a polynomial-time
algorithm that transforms any problem instance into an equivalent one with at
most $(7+3\sqrt{5})k$ variables. Our results are obtained using our improvement
of the Lieberherr-Specker bound above.

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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics