Approximate distance oracles for geometric spanners
Gudmundsson, Joachim ; Levcopoulos, Christos LU
; Narasimhan, Giri
and Smid, Michiel
(2008)
In ACM Transactions on Algorithms
4(1).
- Abstract
- Given an arbitrary real constant epsilon > 0, and a geometric graph G in d-dimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + epsilon)-approximate shortest-path-length queries in constant time. The data structure can be constructed in O( n log n) time using O( n log n) space. This represents the first data structure that answers (1 + epsilon)-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with "rounded" obstacles can be... (More)
- Given an arbitrary real constant epsilon > 0, and a geometric graph G in d-dimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + epsilon)-approximate shortest-path-length queries in constant time. The data structure can be constructed in O( n log n) time using O( n log n) space. This represents the first data structure that answers (1 + epsilon)-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with "rounded" obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer (1 + epsilon)-approximate shortest-path-length queries in constant time for geometric spanner graphs with m = omega(n) edges. The resulting data structure can be constructed in O(m + n log n) time using O(n log n) space. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1428219
- author
- Gudmundsson, Joachim
; Levcopoulos, Christos
LU
; Narasimhan, Giri
and Smid, Michiel
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- geometric graphs, approximation algorithm, Shortest paths, computational geometry, spanners
- in
- ACM Transactions on Algorithms
- volume
- 4
- issue
- 1
- publisher
- Association for Computing Machinery (ACM)
- external identifiers
-
- wos:000265816600010
- scopus:42149179298
- ISSN
- 1549-6333
- DOI
- 10.1145/1328911.1328921
- project
- VR 2005-4085
- language
- English
- LU publication?
- yes
- id
- acd2dec5-1ee2-44fa-bc99-bab2723cb712 (old id 1428219)
- date added to LUP
- 2016-04-01 11:48:36
- date last changed
- 2022-04-20 22:08:56
@article{acd2dec5-1ee2-44fa-bc99-bab2723cb712,
abstract = {{Given an arbitrary real constant epsilon > 0, and a geometric graph G in d-dimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + epsilon)-approximate shortest-path-length queries in constant time. The data structure can be constructed in O( n log n) time using O( n log n) space. This represents the first data structure that answers (1 + epsilon)-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with "rounded" obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer (1 + epsilon)-approximate shortest-path-length queries in constant time for geometric spanner graphs with m = omega(n) edges. The resulting data structure can be constructed in O(m + n log n) time using O(n log n) space.}},
author = {{Gudmundsson, Joachim and Levcopoulos, Christos and Narasimhan, Giri and Smid, Michiel}},
issn = {{1549-6333}},
keywords = {{geometric graphs; approximation algorithm; Shortest paths; computational geometry; spanners}},
language = {{eng}},
number = {{1}},
publisher = {{Association for Computing Machinery (ACM)}},
series = {{ACM Transactions on Algorithms}},
title = {{Approximate distance oracles for geometric spanners}},
url = {{http://dx.doi.org/10.1145/1328911.1328921}},
doi = {{10.1145/1328911.1328921}},
volume = {{4}},
year = {{2008}},
}