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Numerous approximation algorithms for problems on unit disk graphs have beenproposed in the literature, exhibiting a sharp trade-off between running timesand approximation ratios. We introduce a variation of the known shiftingstrategy that allows us to obtain linear-time constant-factor approximationalgorithms for such problems. To illustrate the applicability of the proposedvariation, we obtain results for three well-known optimization problems. Amongsuch results, the proposed method yields linear-time (4+eps)-approximation forthe maximum-weight independent set and the minimum dominating set of unit diskgraphs, thus bringing significant performance improvements when compared toprevious algorithms that achieve the same approximation ratios. Finally, we useaxis-aligned rectangles to illustrate that the same method may be used toderive linear-time approximations for problems on other geometric intersectiongraph classes.

Shifting coresets: obtaining linear-time approximations for unit disk graphs and other geometric intersection graphs