Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to hide a clique?   In the well known planted clique problem, a clique (or alternatively, an
independent set) of size $k$ is planted at random in an Erdos-Renyi random
$G(n, p)$ graph, and the goal is to design an algorithm that finds the maximum
clique (or independent set) in the resulting graph. We introduce a variation on
this problem, where instead of planting the clique at random, the clique is
planted by an adversary who attempts to make it difficult to find the maximum
clique in the resulting graph. We show that for the standard setting of the
parameters of the problem, namely, a clique of size $k = \sqrt{n}$ planted in a
random $G(n, \frac{1}{2})$ graph, the known polynomial time algorithms can be
extended (in a non-trivial way) to work also in the adversarial setting. In
contrast, we show that for other natural settings of the parameters, such as
planting an independent set of size $k=\frac{n}{2}$ in a $G(n, p)$ graph with
$p = n^{-\frac{1}{2}}$, there is no polynomial time algorithm that finds an
independent set of size $k$, unless NP has randomized polynomial time
algorithms.

23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th