An O(log log n) time algorithm to compute the kernel of a polygon

Authors:
Sven Schuierer
Affiliations:
Institut für Informatik, Universität Freiburg, Rheinstr. 10-12, D-79104 Freiburg, Fed. Rep. of Germany
Venue:
Nordic Journal of Computing
Year:
1994

Citing 8
Cited 0

Computational geometry: an introduction

Computational geometry: an introduction
Optimal bounds for decision problems on the CRCW PRAM

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry

Algorithms in combinatorial geometry
Art gallery theorems and algorithms

Art gallery theorems and algorithms
The parallel simplicity of compaction and chaining

Proceedings of the seventeenth international colloquium on Automata, languages and programming
An optimal parallel algorithm for the visibility of a simple polygon from a point

Journal of the ACM (JACM)
An optimal parallel algorithm for detecting weak visibility of a simple polygon

SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An Optimal Algorithm for Finding the Kernel of a Polygon

Journal of the ACM (JACM)

Quantified Score

Hi-index	0.00

Visualization

Abstract

The kernel of a polygon P is the set of all points that see the interior of P. It can be computed as the intersection of the halfplanes that are to the left of the edges of P. We present an O(log log n) time CRCW-PRAM algorithm using n/log log n processors to compute a representation of the kernel of P that allows to answer point containment and line intersection queries efficiently. Our approach is based on computing a subsequence of the edges that are sorted by slope and contain the "relevant" edges for the kernel computation.