TY - GEN

T1 - Reporting intersecting pairs of polytopes in two and three dimensions

AU - Agarwal, Pankaj K.

AU - de Berg, Mark

AU - Har-Peled, Sariel

AU - Overmars, Mark H.

AU - Sharir, Micha

AU - Vahrenhold, Jan

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84958093315&partnerID=8YFLogxK

U2 - 10.1007/3-540-44634-6_12

DO - 10.1007/3-540-44634-6_12

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AN - SCOPUS:84958093315

SN - 3540424237

SN - 9783540424239

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 122

EP - 134

BT - Algorithms and Data Structures - 7th International Workshop, WADS 2001, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Tamassia, Roberto

PB - Springer Verlag

T2 - 7th International Workshop on Algorithms and Data Structures, WADS 2001

Y2 - 8 August 2001 through 10 August 2001

ER -