On the stretch factor of Delaunay triangulations of points in convex position
Computational Geometry: Theory and Applications
Improved local algorithms for spanner construction
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Improved upper bound on the stretch factor of delaunay triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
On bounded degree plane strong geometric spanners
Journal of Discrete Algorithms
Improved local algorithms for spanner construction
Theoretical Computer Science
On certain geometric properties of the Yao---Yao graphs
Journal of Combinatorial Optimization
Hi-index | 0.00 |
We consider the problem of computing spanners of Euclidean and unit disk graphs embedded in the two-dimensional Euclidean plane. We are particularly interested in spanners that possess useful properties such as planarity, bounded degree, and/or light weight. Such spanners have been extensively studied in the area of computational geometry and have been used as the building block for constructing efficient and reliable wireless network communication topologies. We study the above problem under two computational models: the centralized and the distributed model. In the distributed model we focus on algorithms that are local. Such algorithms are suitable for the relevant applications (e.g., wireless computing). Under the centralized model, we present an $O(n\lg n)$ time algorithm that computes a bounded-degree plane spanner of a complete Euclidean graph, where $n$ is the number of points in the graph. Both upper bounds on the degree and the stretch factor significantly improve the previous bounds. We extend this algorithm to compute a bounded-degree plane lightweight spanner of a complete Euclidean graph. Under the distributed model, we give the first local algorithm for computing a spanner of a unit disk graph that is of bounded degree and plane. The upper bounds on the degree, stretch factor, and the locality of the algorithm dramatically improve the previous results, as shown in the paper. This algorithm can also be extended to compute a bounded-degree plane lightweight spanner of a unit disk graph. Our algorithms rely on structural and geometric results that we develop in this paper.