Applications of Geometric Spanner Networks, 2002; Gudmundsson, Levcopoulos, Narasimhan, Smid

2011 ◽  
Keyword(s):  
Geometric Spanner

A GEOMETRIC SPANNER OF SEGMENTS

2010 ◽  
Vol 20 (01) ◽  
pp. 43-67
Author(s):  
JINHUI XU ◽  
YANG YANG ◽  
YONGDING ZHU ◽  
NAOKI KATOH
Keyword(s):  
Computational Geometry ◽  
Efficient Algorithm ◽  
Euclidean Distance ◽  
Dominating Set ◽  
Optimal Solution ◽  
Minimum Size ◽  
Steiner Points ◽  
Separation Ratio ◽  
Geometric Spanner ◽  
Relative Separation

Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider a generalization of the classical geometric spanner problem (called segment spanner): Given a set S of n disjoint 2-D segments, find a spanning network GS with minimum size so that for any pair of points in S, there exists a path in GS with length no more than t times their Euclidean distance. Based on a number of interesting techniques (such as weakly dominating set, strongly dominating set, interval cover, and imaginary Steiner points), we present an efficient algorithm to construct the segment spanner. Our approach first identifies a set Q of Steiner points in S and then constructs a point spanner for the set of Steiner points. Our algorithm runs in O(|Q| + n2 log n) time and Q is a constant approximation (in terms of its size) of the optimal solution when S has a constant relative separation ratio. The approximation ratio depends on the stretch factor t and the relative separation ratio of S.

scholarly journals Applications of Geometric Spanner Networks

2014 ◽  
pp. 1-6
Author(s):  
Joachim Gudmundsson ◽  
Giri Narasimhan ◽  
Michiel Smid
Keyword(s):  
Geometric Spanner

Geometric Spanner Networks

2007 ◽  
Author(s):  
Giri Narasimhan ◽  
Michiel Smid
Keyword(s):  
Geometric Spanner

Geometric Spanner of Segments

2007 ◽  
pp. 75-87 ◽  
Author(s):  
Yang Yang ◽  
Yongding Zhu ◽  
Jinhui Xu ◽  
Naoki Katoh
Keyword(s):  
Geometric Spanner

scholarly journals Applications of Geometric Spanner Networks

2008 ◽  
pp. 40-43 ◽  
Author(s):  
Joachim Gudmundsson ◽  
Giri Narasimhan ◽  
Michiel Smid
Keyword(s):  
Geometric Spanner

scholarly journals Geometric Spanner of Objects under L 1 Distance

2008 ◽  
pp. 395-404
Author(s):  
Yongding Zhu ◽  
Jinhui Xu ◽  
Yang Yang ◽  
Naoki Katoh ◽  
Shin-ichi Tanigawa
Keyword(s):  
Geometric Spanner
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