# Illumination by floodlights

William Steiger, Ileana Streinu

Research output: Contribution to journalArticle

8 Citations (Scopus)

### Abstract

We consider three problems about the illumination of planar regions with floodlights of prescribed angles. Problem 1 is the decision problem: given a wedge W of angle φ ≤ π, n points p1 . . . . . pn in the plane and n angles α1 . . . . . αn such that ∑ni=1 αi ≤ θ, decide whether W can be illuminated by floodlights of angles α1 , . . . , αn placed in some order at the points p1 , . . . , pn and then rotated appropriately. We show that this problem is the exponential time and a specialized version of it (when φ = θ) is in NP. The second problem arises when the n points are in the complementary wedge of W and θ ≥ φ. Boss et al. have shown that a solution exists and gave an O(n log n) algorithm to place the floodlights. Here we give a matching lower bound. Problem 3 involves the illumination of the whole plane. The algorithm of Bose et al. uses an O(n log n) tripartitioning algorithm to reduce problem 3 to problem 2. We give a linear time tripartitioning algorithm of independent interest.

Original language English (US) 57-70 14 Computational Geometry: Theory and Applications 10 1 https://doi.org/10.1016/S0925-7721(97)00027-8 Published - Jan 1 1998

### Fingerprint

Illumination
Lighting
Angle
Wedge
Exponential time
Linear-time Algorithm
Decision problem
Lower bound

### All Science Journal Classification (ASJC) codes

• Computer Science Applications
• Geometry and Topology
• Control and Optimization
• Computational Theory and Mathematics
• Computational Mathematics

### Cite this

Steiger, William ; Streinu, Ileana. / Illumination by floodlights. In: Computational Geometry: Theory and Applications. 1998 ; Vol. 10, No. 1. pp. 57-70.
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Illumination by floodlights. / Steiger, William; Streinu, Ileana.

In: Computational Geometry: Theory and Applications, Vol. 10, No. 1, 01.01.1998, p. 57-70.

Research output: Contribution to journalArticle

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