ISSN:
1432-0541
Keywords:
Arrangements
;
Cuttings
;
Range-searching
;
Dynamization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We consider the half-space range-reporting problem: Given a setS ofn points in ℝd, preprocess it into a data structure, so that, given a query half-space γ, allk points ofS ∩ γ can be reported efficiently. We extend previously known static solutions to dynamic ones, supporting insertions and deletions of points ofS. For a given parameterm,n ≤m ≤n ⌊d/2⌋ and an arbitrarily small positive constant ɛ, we achieveO(m 1+ɛ) space and preprocessing time, O((n/m ⌊d/2⌋ logn+k) query time, and O(m1+ɛn) amortized update time (d ≳ 3). We present, among others, the following applications: an O(n1+ɛ)-time algorithm for computing convex layers in ℝ3, and an output sensitive algorithm for computing a level in an arrangements of planes in ℝ3, whose time complexity is O((b+n) nɛ, whereb is the size of the level.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01293483
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