Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gathering Anonymous, Oblivious Robots on a Grid   We consider a swarm of $n$ autonomous mobile robots, distributed on a
2-dimensional grid. A basic task for such a swarm is the gathering process: All
robots have to gather at one (not predefined) place. A common local model for
extremely simple robots is the following: The robots do not have a common
compass, only have a constant viewing radius, are autonomous and
indistinguishable, can move at most a constant distance in each step, cannot
communicate, are oblivious and do not have flags or states. The only gathering
algorithm under this robot model, with known runtime bounds, needs
$\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time
model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On
the other side, in the case of the 2-dimensional grid, the only known gathering
algorithms for the same time and a similar local model additionally require a
constant memory, states and "flags" to communicate these states to neighbors in
viewing range. They gather in time $\mathcal{O}(n)$.
  In this paper we contribute the (to the best of our knowledge) first
gathering algorithm on the grid that works under the same simple local model as
the above mentioned Euclidean plane strategy, i.e., without memory (oblivious),
"flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time
bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound
matches the time bound of the best known algorithm for the Euclidean plane
mentioned above. We say gathering is done if all robots are located within a
$2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be
solved.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio