On a family of strong geometric spanners that admit local routing strategies

Prosenjit Bose; Paz Carmi; Mathieu Couture; Michiel Smid; Darning Xu

doi:10.1007/978-3-540-73951-7_27

On a family of strong geometric spanners that admit local routing strategies

Prosenjit Bose, Paz Carmi, Mathieu Couture, Michiel Smid, Darning Xu

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

6 Scopus citations

Abstract

We introduce a family of directed geometric graphs, denoted G _λ^θ, that depend on two parameters λ and θ. For 0 < θ < π/2 and 1/2 < λ < 1, the G_λ^θ graph is a strong t-spanner, with t = 1/(1-λ) cos θ. The out-degree of a node in the G _λ^θ graph is at most ⌊2π/ min(θ, arceos 1/2λ)⌋. Moreover, we show that routing can be achieved locally on G_λ^θ. Next, we show that all strong t-spanners are also t-spanners of the unit disk graph. Simulations for various values of the parameters λ and θ indicate that for random point sets, the spanning ratio of G_λ^θ is better than the proven theoretical bounds.

Original language	English
Title of host publication	Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings
Publisher	Springer Verlag
Pages	300-311
Number of pages	12
ISBN (Print)	3540739483, 9783540739487
DOIs	https://doi.org/10.1007/978-3-540-73951-7_27
State	Published - 1 Jan 2007
Externally published	Yes
Event	10th International Workshop on Algorithms and Data Structures, WADS 2007 - Halifax, Canada Duration: 15 Aug 2007 → 17 Aug 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4619 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Workshop on Algorithms and Data Structures, WADS 2007
Country/Territory	Canada
City	Halifax
Period	15/08/07 → 17/08/07

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

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10.1007/978-3-540-73951-7_27

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Bose, P., Carmi, P., Couture, M., Smid, M., & Xu, D. (2007). On a family of strong geometric spanners that admit local routing strategies. In Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings (pp. 300-311). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-73951-7_27

Bose, Prosenjit ; Carmi, Paz ; Couture, Mathieu et al. / On a family of strong geometric spanners that admit local routing strategies. Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag, 2007. pp. 300-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{557d89a8a05b40b298563ea026cfcdf0,

title = "On a family of strong geometric spanners that admit local routing strategies",

abstract = "We introduce a family of directed geometric graphs, denoted G λθ, that depend on two parameters λ and θ. For 0 < θ < π/2 and 1/2 < λ < 1, the Gλθ graph is a strong t-spanner, with t = 1/(1-λ) cos θ. The out-degree of a node in the G λθ graph is at most ⌊2π/ min(θ, arceos 1/2λ)⌋. Moreover, we show that routing can be achieved locally on Gλθ. Next, we show that all strong t-spanners are also t-spanners of the unit disk graph. Simulations for various values of the parameters λ and θ indicate that for random point sets, the spanning ratio of Gλθ is better than the proven theoretical bounds.",

author = "Prosenjit Bose and Paz Carmi and Mathieu Couture and Michiel Smid and Darning Xu",

note = "Funding Information: ✩ An extended abstract of this paper appeared in the Proceedings of the 10th Workshop on Algorithms and Data Structures, 2007. This research was supported in part by NSERC, MITACS, MRI, and HPCVL. * Corresponding author. E-mail address: michiel@scs.carleton.ca (M. Smid).; 10th International Workshop on Algorithms and Data Structures, WADS 2007 ; Conference date: 15-08-2007 Through 17-08-2007",

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doi = "10.1007/978-3-540-73951-7_27",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Bose, P, Carmi, P, Couture, M, Smid, M & Xu, D 2007, On a family of strong geometric spanners that admit local routing strategies. in Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4619 LNCS, Springer Verlag, pp. 300-311, 10th International Workshop on Algorithms and Data Structures, WADS 2007, Halifax, Canada, 15/08/07. https://doi.org/10.1007/978-3-540-73951-7_27

On a family of strong geometric spanners that admit local routing strategies. / Bose, Prosenjit; Carmi, Paz; Couture, Mathieu et al.

Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag, 2007. p. 300-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS).

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

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AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Couture, Mathieu

AU - Smid, Michiel

AU - Xu, Darning

N1 - Funding Information: ✩ An extended abstract of this paper appeared in the Proceedings of the 10th Workshop on Algorithms and Data Structures, 2007. This research was supported in part by NSERC, MITACS, MRI, and HPCVL. * Corresponding author. E-mail address: michiel@scs.carleton.ca (M. Smid).

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We introduce a family of directed geometric graphs, denoted G λθ, that depend on two parameters λ and θ. For 0 < θ < π/2 and 1/2 < λ < 1, the Gλθ graph is a strong t-spanner, with t = 1/(1-λ) cos θ. The out-degree of a node in the G λθ graph is at most ⌊2π/ min(θ, arceos 1/2λ)⌋. Moreover, we show that routing can be achieved locally on Gλθ. Next, we show that all strong t-spanners are also t-spanners of the unit disk graph. Simulations for various values of the parameters λ and θ indicate that for random point sets, the spanning ratio of Gλθ is better than the proven theoretical bounds.

AB - We introduce a family of directed geometric graphs, denoted G λθ, that depend on two parameters λ and θ. For 0 < θ < π/2 and 1/2 < λ < 1, the Gλθ graph is a strong t-spanner, with t = 1/(1-λ) cos θ. The out-degree of a node in the G λθ graph is at most ⌊2π/ min(θ, arceos 1/2λ)⌋. Moreover, we show that routing can be achieved locally on Gλθ. Next, we show that all strong t-spanners are also t-spanners of the unit disk graph. Simulations for various values of the parameters λ and θ indicate that for random point sets, the spanning ratio of Gλθ is better than the proven theoretical bounds.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings

PB - Springer Verlag

T2 - 10th International Workshop on Algorithms and Data Structures, WADS 2007

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ER -

Bose P, Carmi P, Couture M, Smid M, Xu D. On a family of strong geometric spanners that admit local routing strategies. In Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag. 2007. p. 300-311. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-73951-7_27

On a family of strong geometric spanners that admit local routing strategies

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