Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Two-variable Recurrence Relations with Application to
  Parameterized Approximations   In this paper we introduce randomized branching as a tool for parameterized
approximation and develop the mathematical machinery for its analysis. Our
algorithms improve the best known running times of parameterized approximation
algorithms for Vertex Cover and $3$-Hitting Set for a wide range of
approximation ratios. One notable example is a simple parameterized random
$1.5$-approximation algorithm for Vertex Cover, whose running time of
$O^*(1.01657^k)$ substantially improves the best known runnning time of
$O^*(1.0883^k)$ [Brankovic and Fernau, 2013]. For $3$-Hitting Set we present a
parameterized random $2$-approximation algorithm with running time of
$O^*(1.0659^k)$, improving the best known $O^*(1.29^k)$ algorithm of [Brankovic
and Fernau, 2012].
  The running times of our algorithms are derived from an asymptotic analysis
of a wide class of two-variable recurrence relations of the form: $$p(b,k) =
\min_{1\leq j \leq N} \sum_{i=1}^{r_j} \bar{\gamma}_i^j \cdot p(b-\bar{b}^j_i,
k-\bar{k}_i^j),$$ where $\bar{b}^j$ and $\bar{k}^j$ are vectors of natural
numbers, and $\bar{\gamma}^j$ is a probability distribution over $r_j$
elements, for $1\leq j \leq N$. Our main theorem asserts that for any
$\alpha>0$, $$\lim_{k \rightarrow \infty } \frac{1}{k} \log p(\alpha k,k) =
-\max_{1\leq j \leq N} M_j,$$
  where $M_j$ depends only on $\alpha$, $\bar{\gamma}^j$, $\bar{b}^j$ and
$\bar{k}^j$, and can be efficiently calculated by solving a simple numerical
optimization problem. To this end, we show an equivalence between the
recurrence and a stochastic process. We analyze this process using the Method
of Types, by introducing an adaptation of Sanov's theorem to our setting. We
believe our novel analysis of recurrence relations which is of independent
interest is a main contribution of this paper.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin