ORCID

https://orcid.org/0000-0002-7742-0834

Year

2022

Season

Spring

Paper Type

Master's Thesis

College

College of Computing, Engineering & Construction

Degree Name

Master of Science in Computer and Information Sciences (MS)

Department

Computing

NACO controlled Corporate Body

University of North Florida. School of Computing

First Advisor

Dr. Anirban Ghosh

Second Advisor

Dr. Asai Asaithambi

Third Advisor

Dr. Ayan Dutta

Department Chair

Dr. Sherif Elfayoumy

College Dean

Dr. William Klostermeyer

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.

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