Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deploying Wireless Networks with Beeps   We present the \emph{discrete beeping} communication model, which assumes
nodes have minimal knowledge about their environment and severely limited
communication capabilities. Specifically, nodes have no information regarding
the local or global structure of the network, don't have access to synchronized
clocks and are woken up by an adversary. Moreover, instead on communicating
through messages they rely solely on carrier sensing to exchange information.
We study the problem of \emph{interval coloring}, a variant of vertex coloring
specially suited for the studied beeping model. Given a set of resources, the
goal of interval coloring is to assign every node a large contiguous fraction
of the resources, such that neighboring nodes share no resources. To highlight
the importance of the discreteness of the model, we contrast it against a
continuous variant described in [17]. We present an O(1$ time algorithm that
terminates with probability 1 and assigns an interval of size
$\Omega(T/\Delta)$ that repeats every $T$ time units to every node of the
network. This improves an $O(\log n)$ time algorithm with the same guarantees
presented in \cite{infocom09}, and accentuates the unrealistic assumptions of
the continuous model. Under the more realistic discrete model, we present a Las
Vegas algorithm that solves $\Omega(T/\Delta)$-interval coloring in $O(\log n)$
time with high probability and describe how to adapt the algorithm for dynamic
networks where nodes may join or leave. For constant degree graphs we prove a
lower bound of $\Omega(\log n)$ on the time required to solve interval coloring
for this model against randomized algorithms. This lower bound implies that our
algorithm is asymptotically optimal for constant degree graphs.

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The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom