Linear Time Approximation for Dominating Sets and Independent Dominating Sets in Unit Disk Graphs

2013 ◽  
pp. 82-92 ◽  
Author(s):  
Guilherme D. da Fonseca ◽  
Celina M. H. de Figueiredo ◽  
Vinícius G. P. de Sá ◽  
Raphael Machado
Keyword(s):  
Unit Disk ◽  
Linear Time ◽  
Dominating Sets ◽  
Time Approximation ◽  
Unit Disk Graphs

scholarly journals Linear-Time Approximation Algorithms for Unit Disk Graphs

2015 ◽  
pp. 132-143 ◽  
Author(s):  
Guilherme D. da Fonseca ◽  
Vinícius G. Pereira de Sá ◽  
Celina M. H. de Figueiredo
Keyword(s):  
Approximation Algorithms ◽  
Unit Disk ◽  
Linear Time ◽  
Time Approximation ◽  
Unit Disk Graphs

scholarly journals Minimum connected dominating sets and maximal independent sets in unit disk graphs

2006 ◽  
Vol 352 (1-3) ◽  
pp. 1-7 ◽  
Author(s):  
Weili Wu ◽  
Hongwei Du ◽  
Xiaohua Jia ◽  
Yingshu Li ◽  
Scott C.-H. Huang
Keyword(s):  
Unit Disk ◽  
Independent Sets ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Unit Disk Graphs ◽  
Maximal Independent Sets

scholarly journals New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs

2011 ◽  
Vol 412 (3) ◽  
pp. 198-208 ◽  
Author(s):  
Feng Zou ◽  
Yuexuan Wang ◽  
Xiao-Hua Xu ◽  
Xianyue Li ◽  
Hongwei Du ◽  
...  
Keyword(s):  
Unit Disk ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Unit Disk Graphs

scholarly journals Shifting Coresets: Obtaining Linear-Time Approximations for Unit Disk Graphs and Other Geometric Intersection Graphs

2017 ◽  
Vol 27 (04) ◽  
pp. 255-276 ◽  
Author(s):  
Guilherme D. da Fonseca ◽  
Vinícius Gusmão Pereira de Sá ◽  
Celina Miraglia Herrera de Figueiredo
Keyword(s):  
Approximation Algorithms ◽  
Unit Disk ◽  
Optimization Problems ◽  
Linear Time ◽  
Dominating Set ◽  
Independent Set ◽  
Constant Factor ◽  
Intersection Graphs ◽  
Unit Disk Graphs ◽  
Graph Classes

Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy that allows us to obtain linear-time constant-factor approximation algorithms for such problems. To illustrate the applicability of the proposed variation, we obtain results for three well-known optimization problems. Among such results, the proposed method yields linear-time [Formula: see text]-approximations for the maximum-weight independent set and the minimum dominating set of unit disk graphs, thus bringing significant performance improvements when compared to previous algorithms that achieve the same approximation ratios. Finally, we use axis-aligned rectangles to illustrate that the same method may be used to derive linear-time approximations for problems on other geometric intersection graph classes.

scholarly journals Efficient sub-5 approximations for minimum dominating sets in unit disk graphs

2014 ◽  
Vol 540-541 ◽  
pp. 70-81 ◽  
Author(s):  
Guilherme D. da Fonseca ◽  
Celina M.H. de Figueiredo ◽  
Vinícius G. Pereira de Sá ◽  
Raphael C.S. Machado
Keyword(s):  
Unit Disk ◽  
Dominating Sets ◽  
Unit Disk Graphs
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