Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Maxima and Improved Exact Algorithm for MAX-2-SAT   Given a MAX-2-SAT instance, we define a local maximum to be an assignment
such that changing any single variable reduces the number of satisfied clauses.
We consider the question of the number of local maxima that an instance of
MAX-2-SAT can have. We give upper bounds in both the sparse and nonsparse case,
where the sparse case means that there is a bound $d$ on the average number of
clauses involving any given variable. The bounds in the nonsparse case are
tight up to polylogarithmic factors, while in the sparse case the bounds are
tight up to a multiplicative factor in $d$ for large $d$. Additionally, we
generalize to the question of assignments which are maxima up to changing $k>
1$ variables simultaneously; in this case, we give explicit constructions with
large (in a sense explained below) numbers of such maxima in the sparse case.
The basic idea of the upper bound proof is to consider a random assignment to
some subset of the variables and determine the probability that some fraction
of the remaining variables can be fixed without considering interactions
between them. The bounded results hold in the case of weighted MAX-2-SAT as
well. Using this technique and combining with ideas from Ref. 6, we find an
algorithm for weighted MAX-2-SAT which is faster for large $d$ than previous
algorithms which use polynomial space; this algorithm does require an
additional bounds on maximum weights and degree.

37
The categories of this paper are: supr-con
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th