Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum-energy broadcast in random-grid ad-hoc networks: approximation
  and distributed algorithms   The Min Energy broadcast problem consists in assigning transmission ranges to
the nodes of an ad-hoc network in order to guarantee a directed spanning tree
from a given source node and, at the same time, to minimize the energy
consumption (i.e. the energy cost) yielded by the range assignment. Min energy
broadcast is known to be NP-hard.
  We consider random-grid networks where nodes are chosen independently at
random from the $n$ points of a $\sqrt n \times \sqrt n$ square grid in the
plane. The probability of the existence of a node at a given point of the grid
does depend on that point, that is, the probability distribution can be
non-uniform.
  By using information-theoretic arguments, we prove a lower bound
$(1-\epsilon) \frac n{\pi}$ on the energy cost of any feasible solution for
this problem. Then, we provide an efficient solution of energy cost not larger
than $1.1204 \frac n{\pi}$.
  Finally, we present a fully-distributed protocol that constructs a broadcast
range assignment of energy cost not larger than $8n$,thus still yielding
constant approximation. The energy load is well balanced and, at the same time,
the work complexity (i.e. the energy due to all message transmissions of the
protocol) is asymptotically optimal. The completion time of the protocol is
only an $O(\log n)$ factor slower than the optimum. The approximation quality
of our distributed solution is also experimentally evaluated.
  All bounds hold with probability at least $1-1/n^{\Theta(1)}$.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
16
The categories of this paper are: stat