Shifting Coresets: Obtaining Linear-Time Approximations for Unit Disk Graphs and Other Geometric Intersection Graphs - Archive ouverte HAL
Article Dans Une Revue International Journal of Computational Geometry and Applications Année : 2017

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

Résumé

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 (4 + ε)-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.
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Dates et versions

hal-01893789 , version 1 (11-10-2018)

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Guilherme da Fonseca, Vinícius Gusmão Pereira de Sá, Celina Miraglia Herrera de Figueiredo. Shifting Coresets: Obtaining Linear-Time Approximations for Unit Disk Graphs and Other Geometric Intersection Graphs. International Journal of Computational Geometry and Applications, 2017, 27 (04), pp.255 - 276. ⟨10.1142/S0218195917500078⟩. ⟨hal-01893789⟩
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