Bounded-Degree Plane Geometric Spanners in Practice
Authors: 
Frederick Anderson, Anirban Ghosh, Matthew Graham, Lucas Mougeot, David WisnoskyAuthors Info & Claims
Frederick Anderson, Anirban Ghosh, Matthew Graham, Lucas Mougeot, David WisnoskyAuthors Info & ClaimsArticle No.: 1.1, Pages 1 - 36
Abstract
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, 11 algorithms have been designed with various tradeoffs 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, which 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.
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Index Terms
- Bounded-Degree Plane Geometric Spanners in Practice
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Publication History
Published: 08 April 2023
Online AM: 01 February 2023
Accepted: 06 December 2022
Revised: 07 November 2022
Received: 05 May 2022
Published in JEA Volume 28
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