Distributed Planarization and Local Routing Strategies in Sensor Networks
Aubin Jarry, Florian Huc, Pierre Leone, Jose Rolim

TL;DR
This paper introduces an efficient distributed algorithm for constructing a planar 2-spanner in sensor networks, reducing communication overhead and enabling effective local routing with minimal broadcasts.
Contribution
The paper presents a novel distributed algorithm that computes a planar 2-spanner with lower communication complexity and broadcast requirements than previous methods.
Findings
Computes a planar 2-spanner with $6n$ communication complexity.
Requires only $3n$ broadcasts under certain conditions.
Eliminates the need for broadcasts in high-density scenarios.
Abstract
We present an algorithm which computes a planar 2-spanner from an Unit Disk Graph when the node density is sufficient. The communication complexity in terms of number of node's identifier sent by the algorithm is , while the computational complexity is , with the maximum degree of the communication graph. Furthermore, we present a simple and efficient routing algorithm dedicated to the computed graph. Last but not least, using traditional Euclidean coordinates, our algorithm needs the broadcast of as few as node's identifiers. Under the hypothesis of sufficient node density, no broadcast at all is needed, reducing the previous best known complexity of an algorithm to compute a planar spanner of an Unit Disk Graph which was of broadcasts.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Mobile Ad Hoc Networks · Optimization and Search Problems
