TR-197: A Brief Survey of Art Gallery Problems in Integer Lattice Systems

Abstract

The camera placement problem concerns the placement of a fixed number of point-cameras on the integer lattice of d-tuples of integers in order to maximize their visibility. We survey some of the combinatorial optimiza­tion and algorithmic techniques which have been developed in order to study this and other similar problems in the context of lattices and more generally, in combinations of lattice systems and tilings.