# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Fast greedy algorithms for constructing sparse geometric spanners

(2002) In SIAM Journal on Computing 31(5). p.1479-1500
Abstract
Given a set V of n points in R-d and a real constant t > 1, we present the first O(n log n)-time algorithm to compute a geometric t-spanner on V. A geometric t-spanner on V is a connected graph G = ( V, E) with edge weights equal to the Euclidean distances between the endpoints, and with the property that, for all u, v is an element of V the distance between u and v in G is at most t times the Euclidean distance between u and v. The spanner output by the algorithm has O(n) edges and weight O(1).wt (MST), and its degree is bounded by a constant.
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
sparse geometric spanners, cluster graph, computational geometry
in
SIAM Journal on Computing
volume
31
issue
5
pages
1479 - 1500
publisher
Society for Industrial and Applied Mathematics
external identifiers
• wos:000178000900010
• scopus:0036588760
ISSN
0097-5397
DOI
10.1137/S0097539700382947
language
English
LU publication?
yes
id
001bc5c1-af26-4ec1-a682-10492797ae62 (old id 328491)
2016-04-01 16:59:16
date last changed
2021-02-02 03:21:24
```@article{001bc5c1-af26-4ec1-a682-10492797ae62,
abstract     = {Given a set V of n points in R-d and a real constant t &gt; 1, we present the first O(n log n)-time algorithm to compute a geometric t-spanner on V. A geometric t-spanner on V is a connected graph G = ( V, E) with edge weights equal to the Euclidean distances between the endpoints, and with the property that, for all u, v is an element of V the distance between u and v in G is at most t times the Euclidean distance between u and v. The spanner output by the algorithm has O(n) edges and weight O(1).wt (MST), and its degree is bounded by a constant.},
author       = {Gudmundsson, J and Levcopoulos, Christos and Narasimhan, G},
issn         = {0097-5397},
language     = {eng},
number       = {5},
pages        = {1479--1500},
publisher    = {Society for Industrial and Applied Mathematics},
series       = {SIAM Journal on Computing},
title        = {Fast greedy algorithms for constructing sparse geometric spanners},
url          = {http://dx.doi.org/10.1137/S0097539700382947},
doi          = {10.1137/S0097539700382947},
volume       = {31},
year         = {2002},
}

```