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 tspanners 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 tspanners for the visibility graph of P (VG(P), for short) with respect to a holefree 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 (3eps)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 = {186197},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897835},
ISSN = {18688969},
year = {2015},
volume = {34},
editor = {Lars Arge and J{\'a}nos Pach},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5137},
URN = {urn:nbn:de:0030drops51378},
doi = {10.4230/LIPIcs.SOCG.2015.186},
annote = {Keywords: Geometric Spanners, Polygonal Domain, Visibility Graph}
}
2015
Keywords: 

Geometric Spanners, Polygonal Domain, Visibility Graph 
Seminar: 

31st International Symposium on Computational Geometry (SoCG 2015)

Issue date: 

2015 
Date of publication: 

2015 