Union of random minkowski sums and network vulnerability analysis
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Given a range space $(X,\mathcal{R})$, where $\mathcal{R}\subset2^{X}$, the hitting set problem is to find a smallest-cardinality subset H⊆X that intersects each set in $\mathcal{R}$. We present near-linear-time approximation algorithms for the hitting set problem in the following geometric settings: (i) $\mathcal{R}$ is a set of planar regions with small union complexity. (ii) $\mathcal{R}$ is a set of axis-parallel d-dimensional boxes in ℝ d . In both cases X is either the entire ℝ d , or a finite set of points in ℝ d . The approximation factors yielded by the algorithm are small; they are either the same as, or within very small factors off the best factors known to be computable in polynomial time.