There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Realizability of Delaunay triangulations
Information Processing Letters
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Guide to Wireless Sensor Networks
Guide to Wireless Sensor Networks
Survey on Oblivious Routing Strategies
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Greedy Drawings of Triangulations
Discrete & Computational Geometry
Some Results on Greedy Embeddings in Metric Spaces
Discrete & Computational Geometry
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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
The stretch factor of L1- and L∞-delaunay triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
GD'12 Proceedings of the 20th international conference on Graph Drawing
On the spanning ratio of theta-graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We present a deterministic local routing scheme that is guaranteed to find a path between any pair of vertices in a half-θ6-graph whose length is at most 5/√3 = 2.886... times the Euclidean distance between the pair of vertices. The half-θ6-graph is identical to the Delaunay triangulation where the empty region is an equilateral triangle. Moreover, we show that no local routing scheme can achieve a better competitive spanning ratio thereby implying that our routing scheme is optimal. This is somewhat surprising because the spanning ratio of the half-θ6-graph is 2. Since every triangulation can be embedded in the plane as a half-θ6-graph using O(log n) bits per vertex coordinate via Schnyder's embedding scheme (SODA 1990), our result provides a competitive local routing scheme for every such embedded triangulation.