The Maximum Distance-d Independent Set Problem on Unit Disk Graphs

2018 ◽  
pp. 68-80
Author(s):  
Sangram K. Jena ◽  
Ramesh K. Jallu ◽  
Gautam K. Das ◽  
Subhas C. Nandy
Keyword(s):  
Unit Disk ◽  
Independent Set ◽  
Maximum Distance ◽  
Independent Set Problem ◽  
Unit Disk Graphs

scholarly journals Efficient independent set approximation in unit disk graphs

2020 ◽  
Vol 280 ◽  
pp. 63-70 ◽  
Author(s):  
Gautam K. Das ◽  
Guilherme D. da Fonseca ◽  
Ramesh K. Jallu
Keyword(s):  
Unit Disk ◽  
Independent Set ◽  
Unit Disk Graphs ◽  
Set Approximation

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 Sparse hop spanners for unit disk graphs

2021 ◽  
pp. 101808
Author(s):  
Adrian Dumitrescu ◽  
Anirban Ghosh ◽  
Csaba D. Tóth
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs
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