Dynamic half-space range reporting and its applications


Journal Article

We consider the half-space range-reporting problem: Given a set S of n points in ℝd, preprocess it into a data structure, so that, given a query half-space γ, all k points of S ∩ γ can be reported efficiently. We extend previously known static solutions to dynamic ones, supporting insertions and deletions of points of S. For a given parameter m, n ≤m ≤n⌊d/2⌋ and an arbitrarily small positive constant e{open}, we achieve O(m1+e{open}) space and preprocessing time, O((n/m⌊d/2⌋ log n+k) query time, and O(m1+e{open}n) amortized update time (d ≳ 3). We present, among others, the following applications: an O(n1+e{open})-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) ne{open}, where b is the size of the level. © 1995 Springer-Verlag New York Inc.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Matoušek, J

Published Date

  • April 1, 1995

Published In

Volume / Issue

  • 13 / 4

Start / End Page

  • 325 - 345

Electronic International Standard Serial Number (EISSN)

  • 1432-0541

International Standard Serial Number (ISSN)

  • 0178-4617

Digital Object Identifier (DOI)

  • 10.1007/BF01293483

Citation Source

  • Scopus