Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breaking the 2^n-Barrier for Irredundance: A Parameterized Route to
  Solving Exact Puzzles   The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$
and $IR(G)$ respectively, are conceptually linked to domination and
independence numbers and have numerous relations to other graph parameters. It
is a long-standing open question whether determining these numbers for a graph
$G$ on $n$ vertices admits exact algorithms running in time less than the
trivial $\Omega(2^n)$ enumeration barrier. We solve these open problems by
devising parameterized algorithms for the dual of the natural parameterizations
of the problems with running times faster than $O^*(4^{k})$. For example, we
present an algorithm running in time $O^*(3.069^{k})$ for determining whether
$IR(G)$ is at least $n-k$. Although the corresponding problem has been known to
be in FPT by kernelization techniques, this paper offers the first
parameterized algorithms with an exponential dependency on the parameter in the
running time. Additionally, our work also appears to be the first example of a
parameterized approach leading to a solution to a problem in exponential time
algorithmics where the natural interpretation as an exact exponential-time
algorithm fails.

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The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin