College of Computing, Engineering & Construction
Master of Science in Computer and Information Sciences (MS)
NACO controlled Corporate Body
University of North Florida. School of Computing
Dr. Anirban Ghosh
Dr. Asai Asaithambi
Dr. Ayan Dutta
Dr. Sherif Elfayoumy
Dr. William Klostermeyer
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 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 present a simple practical algorithm, named AppxStretchFactor, 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 find that AppxStretchFactor estimates stretch factors almost precisely. Further, it gives 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.
Graham, Matthew Alexander, "Bounded-degree Plane Geometric Spanners: Connecting the Dots Between Theory and Practice" (2022). UNF Graduate Theses and Dissertations. 1122.