2,893 research outputs found
An average case analysis of the minimum spanning tree heuristic for the range assignment problem
We present an average case analysis of the minimum spanning tree heuristic for the range assignment problem on a graph with power weighted edges. It is well-known that the worst-case approximation ratio of this heuristic is 2. Our analysis yields the following results: (1) In the one dimensional case (), where the weights of the edges are 1 with probability and 0 otherwise, the average-case approximation ratio is bounded from above by . (2) When and the distance between neighboring vertices is drawn from a uniform -distribution, the average approximation ratio is bounded from above by where denotes the distance power radient. (3) In Euclidean 2-dimensional space, with distance power gradient , the average performance ratio is bounded from above by
Interference Minimization in Asymmetric Sensor Networks
A fundamental problem in wireless sensor networks is to connect a given set
of sensors while minimizing the \emph{receiver interference}. This is modeled
as follows: each sensor node corresponds to a point in and each
\emph{transmission range} corresponds to a ball. The receiver interference of a
sensor node is defined as the number of transmission ranges it lies in. Our
goal is to choose transmission radii that minimize the maximum interference
while maintaining a strongly connected asymmetric communication graph.
For the two-dimensional case, we show that it is NP-complete to decide
whether one can achieve a receiver interference of at most . In the
one-dimensional case, we prove that there are optimal solutions with nontrivial
structural properties. These properties can be exploited to obtain an exact
algorithm that runs in quasi-polynomial time. This generalizes a result by Tan
et al. to the asymmetric case.Comment: 15 pages, 5 figure
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