Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Dynamic point location in arrangements of hyperplanes
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
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A number of efficient probabilistic algorithms based on the combination of divide-and-conquer and random sampling have been recently discovered. It is shown that all those algorithms can be derandomized with only polynomial overhead. In the process. results of independent interest concerning the covering of hypergraphs are established, and various probabilistic bounds in geometry complexity are improved. For example, given n hyperplanes in d-space and any large enough integer r, it is shown how to compute, in polynomial time, a simplicial packing of size O(r/sup d/) that covers d-space, each of whose simplices intersects O(n/r) hyperplanes. It is also shown how to locate a point among n hyperplanes in d-space in O(log n) query time, using O(n/sup d/) storage and polynomial preprocessing.