Shifting coresets: obtaining linear-time approximations for unit disk graphs and other geometric intersection graphs
Abstract
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+eps)-approximation 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.
Cite
@article{arxiv.1402.4722,
title = {Shifting coresets: obtaining linear-time approximations for unit disk graphs and other geometric intersection graphs},
author = {Guilherme D. da Fonseca and Vinícius G. Pereira de Sá and Celina M. H. de Figueiredo},
journal= {arXiv preprint arXiv:1402.4722},
year = {2016}
}
Comments
An extended abstract of this paper appeared in the 12th Workshop on Approximation and Online Algorithms (WAOA), part of ALGO~2014. The journal version will appear at International Journal of Computational Geometry and Applications