移位核心集：单位圆盘图和其他几何求交图的线性时间近似
Shifting coresets: obtaining linear-time approximations for unit disk graphs and other geometric intersection graphs
摘要：
许多近似算法的问题上的单位圆盘图已被提出在文献中，表现出尖锐的权衡之间的运行时间和近似比。我们介绍了一种变化的已知的移位策略，使我们能够获得线性时间常数因子近似算法这样的问题。为了说明所提出的变化的适用性，我们得到三个著名的优化问题的结果。在这些结果中，所提出的方法产生线性时间（4+eps）近似的最大权重独立集和最小支配集的单位盘图，从而带来显着的性能改善相比，以前的算法，实现相同的近似比。最后，我们使用轴对齐的矩形来说明，同样的方法可以用来获得线性时间近似的问题，其他几何求交图类。
英文摘要：
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.
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