Bounded-degree plane geometric spanners in practice

TL;DR

This paper evaluates various algorithms for constructing bounded-degree plane geometric spanners, introduces a new practical algorithm for estimating stretch factors efficiently, and shares implementation results demonstrating their effectiveness in real-world scenarios.

Contribution

It provides the first practical, efficient algorithm for estimating stretch factors of geometric spanners and offers extensive experimental analysis of existing algorithms in real-world contexts.

Findings

AppxStretchFactor estimates stretch factors almost precisely.

The new algorithm runs linearly in practice for tested pointsets.

Existing algorithms show practical effectiveness in real-world data.

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, 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