Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Pattern Formation in a Ring   Motivated by concerns about diversity in social networks, we consider the
following pattern formation problems in rings. Assume $n$ mobile agents are
located at the nodes of an $n$-node ring network. Each agent is assigned a
colour from the set $\{c_1, c_2, \ldots, c_q \}$. The ring is divided into $k$
contiguous {\em blocks} or neighbourhoods of length $p$. The agents are
required to rearrange themselves in a distributed manner to satisfy given
diversity requirements: in each block $j$ and for each colour $c_i$, there must
be exactly $n_i(j) >0$ agents of colour $c_i$ in block $j$. Agents are assumed
to be able to see agents in adjacent blocks, and move to any position in
adjacent blocks in one time step. When the number of colours $q=2$, we give an
algorithm that terminates in time $N_1/n^*_1 + k + 4$ where $N_1$ is the total
number of agents of colour $c_1$ and $n^*_1$ is the minimum number of agents of
colour $c_1$ required in any block. When the diversity requirements are the
same in every block, our algorithm requires $3k+4$ steps, and is asymptotically
optimal. Our algorithm generalizes for an arbitrary number of colours, and
terminates in $O(nk)$ steps. We also show how to extend it to achieve arbitrary
specific final patterns, provided there is at least one agent of every colour
in every pattern.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ