Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs

2000 ◽  
pp. 194-200 ◽  
Author(s):  
Tomomi Matsui
Keyword(s):  
Approximation Algorithms ◽  
Unit Disk ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Unit Disk Graphs ◽  
Fractional Coloring

Approximation algorithms for maximum independent set of a unit disk graph

2015 ◽  
Vol 115 (3) ◽  
pp. 439-446 ◽  
Author(s):  
Gautam K. Das ◽  
Minati De ◽  
Sudeshna Kolay ◽  
Subhas C. Nandy ◽  
Susmita Sur-Kolay
Keyword(s):  
Approximation Algorithms ◽  
Unit Disk ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Unit Disk Graph

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.

MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS

2010 ◽  
Vol 20 (02) ◽  
pp. 105-118 ◽  
Author(s):  
SERGEY BEREG ◽  
ADRIAN DUMITRESCU ◽  
MINGHUI JIANG
Keyword(s):  
Combinatorial Optimization ◽  
Approximation Algorithms ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Constant Ratio ◽  
Maximum Weight ◽  
Intersection Graphs ◽  
Maximum Area ◽  
Geometric Setting ◽  
Disk Area

Maximum Independent Set (MIS) and its relative Maximum Weight Independent Set (MWIS) are well-known problems in combinatorial optimization; they are NP-hard even in the geometric setting of unit disk graphs. In this paper, we study the Maximum Area Independent Set (MAIS) problem, a natural restricted version of MWIS in disk intersection graphs where the weight equals the disk area. We obtain: (i) Quantitative bounds on the maximum total area of an independent set relative to the union area; (ii) Practical constant-ratio approximation algorithms for finding an independent set with a large total area relative to the union area.

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