#### Document Type

Article

#### Publication Date

1-1-1998

#### Publication Title

Computational Geometry: Theory and Applications

#### 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. © 1998 Elsevier Science B.V.

#### Volume

10

#### Issue

1

#### First Page

57

#### Last Page

70

#### DOI

10.1016/S0925-7721(97)00027-8

#### ISSN

09257721

#### Recommended Citation

Steiger, William and Streinu, Ileana, "Illumination by floodlights" (1998). Computer Science: Faculty Publications, Smith College, Northampton, MA.

https://scholarworks.smith.edu/csc_facpubs/302

## Comments

Archived as published. Open Access article.