On bounded degree plane strong geometric spanners

Prosenjit Bose; Paz Carmi; Lilach Chaitman-Yerushalmi

doi:10.1016/j.jda.2012.03.004

On bounded degree plane strong geometric spanners

Prosenjit Bose
, Paz Carmi
, Lilach Chaitman-Yerushalmi

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

Given a set P of n points in the plane, we show how to compute in O(nlogn) time a spanning subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong plane t-spanner of P with t=(1+√2) ² * δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, the maximum degree bound can be reduced slightly to 6 while remaining a strong plane constant spanner at the cost of an increase in the spanning ratio and no longer being a subgraph of the Delaunay triangulation.

Original language	English
Pages (from-to)	16-31
Number of pages	16
Journal	Journal of Discrete Algorithms
Volume	15
DOIs	https://doi.org/10.1016/j.jda.2012.03.004
State	Published - 1 Aug 2012

Keywords

Computational geometry
Geometric spanners

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jda.2012.03.004

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N2 - Given a set P of n points in the plane, we show how to compute in O(nlogn) time a spanning subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong plane t-spanner of P with t=(1+√2) 2 * δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, the maximum degree bound can be reduced slightly to 6 while remaining a strong plane constant spanner at the cost of an increase in the spanning ratio and no longer being a subgraph of the Delaunay triangulation.

AB - Given a set P of n points in the plane, we show how to compute in O(nlogn) time a spanning subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong plane t-spanner of P with t=(1+√2) 2 * δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, the maximum degree bound can be reduced slightly to 6 while remaining a strong plane constant spanner at the cost of an increase in the spanning ratio and no longer being a subgraph of the Delaunay triangulation.

KW - Computational geometry

KW - Geometric spanners

UR - https://www.scopus.com/pages/publications/84861625536

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JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

ER -

On bounded degree plane strong geometric spanners

Abstract

Keywords

ASJC Scopus subject areas

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