Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Searching of Partial Grids   We consider the following distributed pursuit-evasion problem. A team of
mobile agents called searchers starts at an arbitrary node of an unknown
$n$-node network. Their goal is to execute a search strategy that guarantees
capturing a fast and invisible intruder regardless of its movements using as
few agents as possible. We restrict our attention to networks that are embedded
into partial grids: nodes are placed on the plane at integer coordinates and
only nodes at distance one can be adjacent. We give a distributed algorithm for
the searchers that allow them to compute a connected and monotone strategy that
guarantees searching any unknown partial grid with the use of $O(\sqrt{n})$
searchers. As for a lower bound, not only there exist partial grids that
require $\Omega(\sqrt{n})$ searchers, but we prove that for each distributed
searching algorithm there is a partial grid that forces the algorithm to use
$\Omega(\sqrt{n})$ searchers but $O(\log n)$ searchers are sufficient in the
offline scenario. This gives a lower bound of $\Omega(\sqrt{n}/\log n)$ in
terms of achievable competitive ratio of any distributed algorithm.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin