@inproceedings{2dc626d9229344e7ac6655f28f0398af,

title = "Reporting intersecting pairs of polytopes in two and three dimensions",

abstract = "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.",

author = "Agarwal, {Pankaj K.} and {de Berg}, Mark and Sariel Har-Peled and Overmars, {Mark H.} and Micha Sharir and Jan Vahrenhold",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2001.; null ; Conference date: 08-08-2001 Through 10-08-2001",

year = "2001",

doi = "10.1007/3-540-44634-6_12",

language = "אנגלית",

isbn = "3540424237",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "122--134",

editor = "Frank Dehne and Jorg-Rudiger Sack and Roberto Tamassia",

booktitle = "Algorithms and Data Structures - 7th International Workshop, WADS 2001, Proceedings",

}