Computing the greedy spanner in linear space

S.P.A. Alewijnse; Q.W. Bouts; A.P. Brink, ten; K. Buchin

doi:10.1007/978-3-642-40450-4_4

Computing the greedy spanner in linear space

S.P.A. Alewijnse, Q.W. Bouts, A.P. Brink, ten, K. Buchin

Algorithms

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

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
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	https://doi.org/10.1007/978-3-642-40450-4_4
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
Volume	8125
ISSN (Print)	0302-9743

Conference

Conference	21st Annual European Symposium on Algorithms (ESA 2013)
Abbreviated title	ESA 2013
Country	France
City	Sophia Antipolis
Period	2/09/13 → 4/09/13
Internet address	http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html

Access to Document

10.1007/978-3-642-40450-4_4

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

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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.",

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Alewijnse, SPA, Bouts, QW, Brink, ten, AP & Buchin, K 2013, Computing the greedy spanner in linear space. in HL Bodlaender & GF Italiano (eds), Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings). Lecture Notes in Computer Science, vol. 8125, Springer, Berlin, pp. 37-48, 21st Annual European Symposium on Algorithms (ESA 2013), Sophia Antipolis, France, 2/09/13. https://doi.org/10.1007/978-3-642-40450-4_4

Computing the greedy spanner in linear space. / Alewijnse, S.P.A.; Bouts, Q.W.; Brink, ten, A.P.; Buchin, K.

Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings). ed. / H.L. Bodlaender; G.F. Italiano. Berlin : Springer, 2013. p. 37-48 (Lecture Notes in Computer Science; Vol. 8125).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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