Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on Max Lin-2 above Average   In the Max Lin-2 problem we are given a system $S$ of $m$ linear equations in
$n$ variables over $\mathbb{F}_2$ in which Equation $j$ is assigned a positive
integral weight $w_j$ for each $j$. We wish to find an assignment of values to
the variables which maximizes the total weight of satisfied equations. This
problem generalizes Max Cut. The expected weight of satisfied equations is
$W/2$, where $W=w_1+... +w_m$; $W/2$ is a tight lower bound on the optimal
solution of Max Lin-2.
  Mahajan et al. (J. Comput. Syst. Sci. 75, 2009) stated the following
parameterized version of Max Lin-2: decide whether there is an assignment of
values to the variables that satisfies equations of total weight at least
$W/2+k$, where $k$ is the parameter. They asked whether this parameterized
problem is fixed-parameter tractable, i.e., can be solved in time
$f(k)(nm)^{O(1)}$, where $f(k)$ is an arbitrary computable function in $k$
only. Their question remains open, but using some probabilistic inequalities
and, in one case, a Fourier analysis inequality, Gutin et al. (IWPEC 2009)
proved that the problem is fixed-parameter tractable in three special cases.
  In this paper we significantly extend two of the three special cases using
only tools from combinatorics. We show that one of our results can be used to
obtain a combinatorial proof that another problem from Mahajan et al. (J.
Comput. Syst. Sci. 75, 2009), Max $r$-SAT above the Average, is fixed-parameter
tractable for each $r\ge 2.$ Note that Max $r$-SAT above the Average has been
already shown to be fixed-parameter tractable by Alon et al. (SODA 2010), but
the paper used the approach of Gutin et al. (IWPEC 2009).

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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom