Cooperative half-guards in art galleries

TL;DR

This paper proves optimal guard placement strategies with 180-degree vision in simple polygonal art galleries, ensuring full coverage and connectivity, with specific improvements for orthogonal galleries.

Contribution

It establishes tight bounds for half-guard placement in simple and orthogonal galleries, extending classical art gallery problem results.

Findings

Optimal guard placement bounds are proven for simple galleries.

Improved bounds are provided for orthogonal galleries.

The bounds match known results for full-vision guards.

Abstract

In any simple polygonal art gallery with n walls, we show that it is possible to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way that every interior point of the gallery can be seen by one of them, and such that the mutual visibility graph formed by the guards is connected. This upper bound is tight, in that there exist galleries which require this number of guards, and equals the known result for guards with full 360 degree range of vision. We also show that for orthogonal art galleries, this result may be improved to floor(n/2)-2 guards with 180 degree range of vision.