Translating a Planar Object to Maximize Point Containment
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Efficient data reduction with EASE
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Detecting cuts in sensor networks
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Detecting cuts in sensor networks
ACM Transactions on Sensor Networks (TOSN)
The 2-center problem in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Approximate Halfspace Range Counting
SIAM Journal on Computing
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We introduce the concept of a {\em sensitive $\varepsilon$-approximation} and use it to derive a more efficient algorithm for computing $\varepsilon$-nets. We define and investigate product range spaces, for which we establish sampling theorems analogous to the standard finite VC-dimensional case. This generalizes and simplifies results from previous works. Using these tools, we give a new deterministic algorithm for computing the convex hull of n points in $\mbox{\smallBbb R}^d$. The algorithm is obtained by derandomization of a randomized incremental algorithm, and its running time of O(nlog n + n{\lfloor d/2\rfloor})$ is optimal for any fixed dimension $d\geq 2$.