Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A polynomial time circle packing algorithm
Discrete Mathematics
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Computational Geometry: Theory and Applications
Topology control in wireless ad hoc and sensor networks
ACM Computing Surveys (CSUR)
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Distributed computation of virtual coordinates
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Greedy drawings of triangulations
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct Greedy Graph Drawing in the Hyperbolic Plane
Graph Drawing
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A generalized greedy routing algorithm for 2-connected graphs
Theoretical Computer Science
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Greedy routing via embedding graphs onto semi-metric spaces
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
On succinct convex greedy drawing of 3-connected plane graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Schnyder greedy routing algorithm
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
An optimal greedy routing algorithm for triangulated polygons
Computational Geometry: Theory and Applications
A simple routing algorithm based on Schnyder coordinates
Theoretical Computer Science
Greedy routing via embedding graphs onto semi-metric spaces
Theoretical Computer Science
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Greedy routing protocols for wireless sensor networks (WSNs) are fast and efficient but in general cannot guarantee message delivery. Hence researchers are interested in the problem of embedding WSNs in low dimensional space (e.g., R2) in a way that guarantees message delivery with greedy routing. It is well known that Delaunay triangulations are such embeddings. We present the algorithm FindAngles, which is a fast, simple, local distributed algorithm that computes a Delaunay triangulation from any given combinatorial graph that is Delaunay realizable. Our algorithm is based on a characterization of Delaunay realizability due to Hiroshima et al. (IEICE 2000). When compared to the PowerDiagram algorithm of Chen et al. (SoCG 2007), our algorithm requires on average 1/7th the number of iterations, scales better to larger networks, and has a much faster distributed implementation. The PowerDiagram algorithm was proposed as an improvement on another algorithm due to Thurston (unpublished, 1988). Our experiments show that on average the PowerDiagram algorithm uses about 18% fewer iterations than the Thurston algorithm, whereas our algorithm uses about 88% fewer iterations. Experimentally, FindAngles exhibits well behaved convergence. Theoretically, we prove that with certain initial conditions the error term decreases monotonically. Taken together, these suggest our algorithm may have polynomial time convergence for certain classes of graphs. We note that our algorithm runs only on Delaunay realizable triangulations. This is not a significant concern because Hiroshima et al. (IEICE 2000) indicate that most combinatorial triangulations are indeed Delaunay realizable, which we have also observed experimentally.