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

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 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.

Linear time-approximation algorithms for bin packing

2000 ◽  
Vol 26 (5) ◽  
pp. 217-222 ◽  
Author(s):  
Guochuan Zhang ◽  
Xiaoqiang Cai ◽  
C.K. Wong
Keyword(s):  
Approximation Algorithms ◽  
Bin Packing ◽  
Linear Time ◽  
Time Approximation

APPROXIMATING THE DIAMETER, WIDTH, SMALLEST ENCLOSING CYLINDER, AND MINIMUM-WIDTH ANNULUS

2002 ◽  
Vol 12 (01n02) ◽  
pp. 67-85 ◽  
Author(s):  
TIMOTHY M. CHAN
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Optimization Problems ◽  
Linear Time ◽  
Minimum Width ◽  
Time Approximation ◽  
Running Time ◽  
Fixed Dimension ◽  
Smallest Enclosing Cylinder ◽  
Point Set

We study (1+ε)-factor approximation algorithms for several well-known optimization problems on a given n-point set: (a) diameter, (b) width, (c) smallest enclosing cylinder, and (d) minimum-width annulus. Among our results are new simple algorithms for (a) and (c) with an improved dependence of the running time on ε, as well as the first linear-time approximation algorithm for (d) in any fixed dimension. All four problems can be solved within a time bound of the form O(n+ε-c) or O(n log (1/ε)+ε-c).

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