On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Submatrix maximum queries in Monge matrices and Monge partial matrices, and their applications
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Finding the maximal empty disk containing a query point
Proceedings of the twenty-eighth annual symposium on Computational geometry
Finding the maximal empty disk containing a query point
Proceedings of the twenty-eighth annual symposium on Computational geometry
Localized geometric query problems
Computational Geometry: Theory and Applications
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Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log2n), and a query takes O(log2n) time.