Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Experimental Algorithm for the Maximum Independent Set Problem   We develop an experimental algorithm for the exact solving of the maximum
independent set problem. The algorithm consecutively finds the maximal
independent sets of vertices in an arbitrary undirected graph such that the
next such set contains more elements than the preceding one. For this purpose,
we use a technique, developed by Ford and Fulkerson for the finite partially
ordered sets, in particular, their method for partition of a poset into the
minimum number of chains with finding the maximum antichain. In the process of
solving, a special digraph is constructed, and a conjecture is formulated
concerning properties of such digraph. This allows to offer of the solution
algorithm. Its theoretical estimation of running time equals to is $O(n^{8})$,
where $n$ is the number of graph vertices. The offered algorithm was tested by
a program on random graphs. The testing the confirms correctness of the
algorithm.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ