Point Location in Arrangements of Hyperplanes
نویسندگان
چکیده
منابع مشابه
A note on point location in arrangements of hyperplanes
We give an algorithm for point location in an arrangement of hyperplanes in with running time and space . The space improves on the bound of Meiser’s algorithm [5] that has a similar running time.
متن کاملDecomposing arrangements of hyperplanes: VC-dimension, combinatorial dimension, and point location
This work is motivated by several basic problems and techniques that rely on space decomposition of arrangements of hyperplanes in high-dimensional spaces, most notably Meiser’s 1993 algorithm for point location in such arrangements. A standard approach to these problems is via random sampling, in which one draws a random sample of the hyperplanes, constructs a suitable decomposition of its arr...
متن کاملPoint Location Among Hyperplanes and Unidirectional Ray-shooting
We present an algorithm for locating a query point q in an arrangement of n hyperplanes in Rd. The size of the data structure is O(n”) and the time to answer any query is O(log n). Unlike previous data structures, our solution will also report, in addition to the face of the arrangement that contains q, the first hyperplane that is hit (if any) by shooting the point q in some fixed direction. A...
متن کاملPoint Location in Zones of K-flats in Arrangements
Let A( H) be the arrangement of a set H of n hyperplanes in d-space. A k-flat is defined to be a k-dimensional affine subspace of d-space. The zone of a k-flat 1 with respect to H is the closure of all cells in A(H) that intersect I. In this paper we study some problems on zones of k-flats. Our most important result is a data structure for point location in the zone of a k-flat. This structure ...
متن کاملInductively Factored Signed-graphic Arrangements of Hyperplanes
In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.
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ژورنال
عنوان ژورنال: Information and Computation
سال: 1993
ISSN: 0890-5401
DOI: 10.1006/inco.1993.1057