The Floodlight Problem-Reference-Cited by-同舟云学术

The Floodlight Problem

Published:1997-02 Issue:01n02 Volume:07 Page:153-163
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

Bose Prosenjit¹,Guibas Leonidas²,Lubiw Anna³,Overmars Mark⁴,Souvaine Diane⁵,Urrutia Jorge⁶

Affiliation:

1. Dept. Computer Science, McGill Univ., Montreal, H3A 2A7, Canada

2. Computer Science Dept., Stanford Univ., Palo Alto, California, 94305, USA

3. Dept. Computer Science, Univ. of Waterloo, Waterloo, N2L 3G1, Canada

4. Dept. Comp. Sc., Univ. of Utrecht, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands

5. Dept. Computer Science, Rutgers Univ., New Brunswick, New Jersey, 08903, USA

6. Dept. of Computer Science, Univ. of Ottawa, Ottawa, Ontario, K1N 6N5, Canada

Abstract

Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(n log n) algorithms for both these problems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195997000090

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