### Abstract

The greedy spanner is a high-quality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner of n points use O(n2) space, which is impractical on large instances. To the best of our knowledge, the largest instance for which the greedy spanner was computed so far has about 13,000 vertices.
We present a O(n)-space algorithm that computes the same spanner for points in Rd running in O(n2 log2n) time for any fixed stretch factor and dimension. We discuss and evaluate a number of optimizations to its running time, which allowed us to compute the greedy spanner on a graph with a million vertices. To our knowledge, this is also the first algorithm for the greedy spanner with a near-quadratic running time guarantee that has actually been implemented.

Original language | English |
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Title of host publication | Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings) |

Editors | H.L. Bodlaender, G.F. Italiano |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 37-48 |

ISBN (Print) | 978-3-642-40449-8 |

DOIs | |

Publication status | Published - 2013 |

Event | 21st Annual European Symposium on Algorithms (ESA 2013) - Sophia Antipolis, France Duration: 2 Sep 2013 → 4 Sep 2013 Conference number: 21st http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 8125 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 21st Annual European Symposium on Algorithms (ESA 2013) |
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Abbreviated title | ESA 2013 |

Country | France |

City | Sophia Antipolis |

Period | 2/09/13 → 4/09/13 |

Internet address |

## Cite this

Alewijnse, S. P. A., Bouts, Q. W., Brink, ten, A. P., & Buchin, K. (2013). Computing the greedy spanner in linear space. In H. L. Bodlaender, & G. F. Italiano (Eds.),

*Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings)*(pp. 37-48). (Lecture Notes in Computer Science; Vol. 8125). Springer. https://doi.org/10.1007/978-3-642-40450-4_4