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Constructing Doppelgängers of Greedy Geometric Spanners in Practice

Author Anirban Ghosh

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LIPIcs.SoCG.2026.53.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • geometric graph
  • geometric spanners
  • greedy spanners
  • algorithm engineering

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Abstract

Greedy geometric spanners are considered to be the gold standard for their near-optimal guarantees in terms of sparsity and total weight. However, their inefficient construction poses significant challenges for large-scale geometric networks, especially for low values of stretch factors (< 2). We present Θ-Greedy, a simple and practical parallel algorithm engineered for constructing doppelgängers of greedy geometric spanners that empirically resemble the greedy spanners in key structural and performance metrics, including average degree, degree, and lightness. Unlike approximate greedy spanners, doppelgängers of greedy spanners are almost indistinguishable from the actual greedy spanners in practice.
In our experiments, Θ-Greedy consistently produced greedy spanner doppelgängers across a broad range of synthetic and real-world datasets, offering the first practical alternative to the computationally intensive greedy spanners. Θ-Greedy can construct a 1.1-spanner on a 128K-element uniformly distributed point set in well under 5 minutes. In contrast, Bucketing, the most practical greedy spanner algorithm, takes around 3 hours. For million-sized point sets, Θ-Greedy can run to completion in a few hours, making it much faster than Bucketing, which takes days to finish. In extensive experiments on synthetic and real-world datasets, Θ-Greedy delivered speedups of up to 147x over Bucketing while preserving greedy-like sparsity and weight. 
For broader uses of the algorithm and reproducibility, we share our engineered C++ code.

Cite As Get BibTex

Anirban Ghosh. Constructing Doppelgängers of Greedy Geometric Spanners in Practice. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.53

Author Details

Anirban Ghosh
  • University of North Florida, Jacksonville, FL, USA

Acknowledgements

The author would like to thank the anonymous reviewers for their insightful comments and suggestions, which helped to significantly improve the clarity and quality of this paper.

Supplementary Materials

References

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