Computing the greedy spanner in near-quadratic time

Prosenjit Bose; Paz Carmi; Mohammad Farshi; Anil Maheshwari; Michiel Smid

doi:10.1007/s00453-009-9293-4

Computing the greedy spanner in near-quadratic time

Prosenjit Bose, Paz Carmi, Mohammad Farshi, Anil Maheshwari, Michiel Smid

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

27 Scopus citations

Abstract

The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n ²log n) time. Since computing the greedy spanner has an Ω(n ²) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.

Original language	English
Pages (from-to)	711-729
Number of pages	19
Journal	Algorithmica
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s00453-009-9293-4
State	Published - 1 Nov 2010
Externally published	Yes

Keywords

Dilation
Doubling dimension
Greedy algorithm
Spanner
Stretch factor

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-009-9293-4

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title = "Computing the greedy spanner in near-quadratic time",

abstract = "The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n 2log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.",

keywords = "Dilation, Doubling dimension, Greedy algorithm, Spanner, Stretch factor",

author = "Prosenjit Bose and Paz Carmi and Mohammad Farshi and Anil Maheshwari and Michiel Smid",

note = "Funding Information: Research supported in part by NSERC and MRI.",

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AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Farshi, Mohammad

AU - Maheshwari, Anil

AU - Smid, Michiel

N1 - Funding Information: Research supported in part by NSERC and MRI.

PY - 2010/11/1

Y1 - 2010/11/1

N2 - The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n 2log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.

AB - The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n 2log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.

KW - Dilation

KW - Doubling dimension

KW - Greedy algorithm

KW - Spanner

KW - Stretch factor

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EP - 729

JO - Algorithmica

JF - Algorithmica

IS - 3

ER -

Computing the greedy spanner in near-quadratic time

Abstract

Keywords

ASJC Scopus subject areas

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