License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SOCG.2015.186
URN: urn:nbn:de:0030-drops-51378
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5137/
Abam, Mohammad Ali ;
Adeli, Marjan ;
Homapour, Hamid ;
Asadollahpoor, Pooya Zafar
Geometric Spanners for Points Inside a Polygonal Domain
Abstract
Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function d where for any two points p and q, d(p,q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h=0), we construct a (sqrt(10)+eps)-spanner that has O(n log^2 n) edges where eps is the a given positive real number. For a case where there are h holes, our construction gives a (5+eps)-spanner with the size of O(sqrt(h) n log^2 n).
Moreover, we study t-spanners for the visibility graph of P (VG(P), for short) with respect to a hole-free polygonal domain D. The graph VG(P) is not necessarily a complete graph or even connected. In this case, we propose an algorithm that constructs a (3+eps)-spanner of size almost O(n^{4/3}). In addition, we show that there is a set P of n points such that any (3-eps)-spanner of VG(P) must contain almost n^2 edges.
BibTeX - Entry
@InProceedings{abam_et_al:LIPIcs:2015:5137,
author = {Mohammad Ali Abam and Marjan Adeli and Hamid Homapour and Pooya Zafar Asadollahpoor},
title = {{Geometric Spanners for Points Inside a Polygonal Domain}},
booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)},
pages = {186--197},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-83-5},
ISSN = {1868-8969},
year = {2015},
volume = {34},
editor = {Lars Arge and J{\'a}nos Pach},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5137},
URN = {urn:nbn:de:0030-drops-51378},
doi = {10.4230/LIPIcs.SOCG.2015.186},
annote = {Keywords: Geometric Spanners, Polygonal Domain, Visibility Graph}
}
|
Keywords: |
|
Geometric Spanners, Polygonal Domain, Visibility Graph |
|
Collection: |
|
31st International Symposium on Computational Geometry (SoCG 2015) |
|
Issue Date: |
|
2015 |
|
Date of publication: |
|
12.06.2015 |
