Normal art galleries: wall in - all in

TL;DR

This paper introduces the concept of normal galleries, characterizes certain classes as normal, and provides a polynomial-time algorithm to verify guard configurations that cover walls but not the entire gallery.

Contribution

It defines normal galleries, proves that star galleries and galleries with up to two reflex corners are normal, and offers an efficient algorithm for guard coverage verification.

Findings

Star galleries are normal.

Galleries with up to two reflex corners are normal.

Efficient algorithm for guard coverage verification.

Abstract

We introduce the notion of a normal gallery, a gallery in which any configuration of guards that visually covers the walls covers the entire gallery. We show that any star gallery is normal and any gallery with at most two reflex corners is normal. A polynomial time algorithm is provided deciding if, for a given polygon and a finite set of positions, there exists a configuration of guards in some of these positions that visually covers the walls but not the entire gallery.