Reporting intersecting pairs of polytopes in two and three dimensions


Conference Paper

© Springer-Verlag Berlin Heidelberg 2001. Let P = {P1,…, Pm} be a set of m convex polytopes in Rd, for d = 2, 3, with a total of n vertices. We present output-sensitive algorithms for reporting all k pairs of indices (i, j) such that Piintersects Pj. For the planar case we describe a simple algorithm with running time O(n4/3log n + k), and an improved randomized algorithm with expected running time O((n logm + k)α(n) log n) (which is faster for small values of k). For d = 3, we present an O(n8/5+ε+ k)-time algorithm, for any ε > 0. Our algorithms can be modified to count the number of intersecting pairs in O(n4/3logO(1) n) time for the planar case, and in O(n8/5+ε) time and R3.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; de Berg, M; Har-Peled, S; Overmars, MH; Sharir, M; Vahrenhold, J

Published Date

  • January 1, 2001

Published In

Volume / Issue

  • 2125 /

Start / End Page

  • 122 - 134

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

International Standard Book Number 10 (ISBN-10)

  • 3540424237

International Standard Book Number 13 (ISBN-13)

  • 9783540424239

Digital Object Identifier (DOI)

  • 10.1007/3-540-44634-6_12

Citation Source

  • Scopus