Emanation Graph: A Plane Geometric Spanner with Steiner Points

An emanation graph of grade k on a set points is plane spanner made by shooting $$2^{k+1}$$ equally spaced rays from each point, where the shorter stop longer ones upon collision. The collision are Steiner spanner. Emanation graphs one were studied Mondal and Nachmanson in context network visualization. They proved that spanning ratio such bounded $$(2+\sqrt{2})\approx 3.414$$ . We improve this upper bound to $$\sqrt{10} \approx 3.162$$ show be tight, i.e., there exist with $$\sqrt{10}$$ for every fixed k, constant spanners, factor depends k. two may have twice number edges compared graphs. Hence we introduce heuristic method simplifying them. In particular, compare simplified against Shewchuk’s constrained Delaunay triangulations both synthetic real-life datasets. Our experimental results reveal outperform common quality measures (e.g., edge count, angular resolution, average degree, total length) while maintaining comparable point count.