Art Gallery and Illumination Problems

How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully na¨ıve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O'Rourke published his book Art Gallery Theorems and Algorithms which has further fueled this area of research. The present book is being written almost 10 years since the publication of O'Rourke's book, and the need for an up-to-date manuscript on Art Gallery or Illumination Problems is evident. Some important open problems stated in O'Rourke's book, such as ... have been solved. New directions of research have since been investigated, including: watchman routes, floodlight illumination problems, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others. In this book, we study these results and try to give a complete overview of all the results known to us. We hope that this book will provide a renewed source of inspiration towards the study of Art Gallery Problems.