On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Approximation algorithms for layered manufacturing
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Cache-oblivious range reporting with optimal queries requires superlinear space
Proceedings of the twenty-fifth annual symposium on Computational geometry
Hi-index | 0.00 |
Given n points in three dimensions, we show how to answer halfspace range reporting queries in O(log n + k) expected time for an output size k. Our data structure can be preprocessed in optimal O(n log n) expected time. We apply this result to obtain the first optimal randomized algorithm for the construction of the (\le k)-level in an arrangement of n planes in three dimensions. The algorithm runs in O(n log n + nk^2) expected time. Our techniques are based on random sampling. Applications in two dimensions include an improved data structure for "k nearest neighbors" queries, and an algorithm that constructs the order-k Voronoi diagram in O(n log n + nklog k) expected time.