Bounded-degree Plane Geometric Spanners in Practice

The construction of bounded-degree plane geometric spanners has been a focus of interest since 2002 when Bose, Gudmundsson, and Smid proposed the first algorithm to construct such spanners. To date, eleven algorithms have been designed with various trade-offs in degree and stretch-factor. We have implemented these sophisticated spanner algorithms in C++ using the CGAL library and experimented with them using large synthetic and real-world pointsets. Our experiments have revealed their practical behavior and real-world efficacy. We share the implementations via GitHub for broader uses and future research. We design and engineer EstimateStretchFactor, a simple practical algorithm, that can estimate stretch-factors (obtains lower bounds on the exact stretch-factors) of geometric spanners – a challenging problem for which no practical algorithm is known yet. In our experiments with bounded-degree plane geometric spanners, we found that EstimateStretchFactor estimated stretch-factors almost precisely. Further, it gave linear runtime performance in practice for the pointset distributions considered in this work, making it much faster than the naive Dijkstra-based algorithm for calculating stretch-factors.