Constructing Levels in Arrangements and Higher Order Voronoi Diagrams

Journal Article (Journal Article)

We give simple randomized incremental algorithms for computing the ≤κ-level in an arrangement of n lines in the plane or in an arrangement of n planes in ℝ3. The expected running time of our algorithms is O(nκ + nα(n) logn) for the planar case and O(nκ2 + nlog3n) for the three-dimensional case. Both bounds are optimal unless κ is very small. The algorithm generalizes to computing the ≤κ-level in an arrangement of discs or x-monotone Jordan curves in the plane. Our approach can also compute the κ-level; this yields a randomized algorithm for computing the order-κ Voronoi diagram of n points in the plane in expected time O(κ(n - κ) log n + n log3 n).

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; De Berg, M; Matoušek, J; Schwarzkopf, O

Published Date

  • January 1, 1998

Published In

Volume / Issue

  • 27 / 3

Start / End Page

  • 654 - 667

International Standard Serial Number (ISSN)

  • 0097-5397

Digital Object Identifier (DOI)

  • 10.1137/S0097539795281840

Citation Source

  • Scopus