Paper Info
Title
Approximating the edge length of 2-edge connected planar geometric graphs on a set of points
Abstract
Given a set P of n points in the plane, we solve the problems of constructing a geometric planar graph spanning P 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set P, respectively. First, we construct in O(nlogn) time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in O(nlogn) time a 2-edge connected geometric planar graph spanning P with max edge length bounded by √5 times the optimal, assuming that the set P forms a connected Unit Disk Graph. Second, we prove that 2 times the optimal is always sufficient if the set of points forms a 2 edge connected Unit Disk Graph and give an algorithm that runs in O(n2) time. We also show that for k ∈ O(√n), there exists a set P of n points in the plane such that even though the Unit Disk Graph spanning P is k-vertex connected, there is no 2-edge connected geometric planar graph spanning P even if the length of its edges is allowed to be up to 17/16.
Year
DOI
Venue
2012
10.1007/978-3-642-29344-3_22
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Keywords
DocType
Volume
connected unit disk,minimum degree,unit disk graph,geometric planar graph,2-edge connected geometric planar,connected planar geometric graph,appropriate connectivity condition,set p,max edge length,n point
Conference
abs/1112.3523
ISSN
Citations 
PageRank 
0302-9743
2
0.41
References 
Authors
13
5
Name
Order
Citations
PageRank
Stefan Dobrev152841.68
Evangelos Kranakis23107354.48
Danny Krizanc31778191.04
Oscar Morales-Ponce4232.89
Ladislav Stacho525935.64