Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The algorithm by Ferson et al. is surprisingly fast: An NP-hard
  optimization problem solvable in almost linear time with high probability   We start with the algorithm of Ferson et al. (\emph{Reliable computing} {\bf
11}(3), p.~207--233, 2005), designed for solving a certain NP-hard problem
motivated by robust statistics.
  First, we propose an efficient implementation of the algorithm and improve
its complexity bound to $O(n \log n+n\cdot 2^\omega)$, where $\omega$ is the
clique number in a certain intersection graph. Then we treat input data as
random variables (as it is usual in statistics) and introduce a natural
probabilistic data generating model. On average, we get $2^\omega =
O(n^{1/\log\log n})$ and $\omega = O(\log n / \log\log n)$. This results in
average computing time $O(n^{1+\epsilon})$ for $\epsilon > 0$ arbitrarily
small, which may be considered as ``surprisingly good'' average time complexity
for solving an NP-hard problem. Moreover, we prove the following tail bound on
the distribution of computation time: ``hard'' instances, forcing the algorithm
to compute in time $2^{\Omega(n)}$, occur rarely, with probability tending to
zero faster than exponentially with $n \rightarrow \infty$.

25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph