# Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles

## Abstract

*Embedding planar graphs on the grid*, in Proceedings of the 1st Annual ACM--SIAM Symposium on Discrete Algorithms (SODA 1990), ACM, New York, SIAM, Philadelphia, 1990, pp. 138--148], our result provides a competitive local routing algorithm for every such embedded triangulation. Finally, we show how our routing algorithm can be adapted to provide a routing ratio of $15/\sqrt{3} \approx 8.660$ on two bounded degree subgraphs of the half-$\theta_6$-graph.

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#### History

**Submitted**: 23 September 2014

**Accepted**: 14 August 2015

**Published online**: 3 November 2015

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