Mobile vs. point guards

Abstract

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Furthermore, we show that the latter two numbers can be calculated in linear time.

This version covers a previously missing case in both Phase 2 & 3

References in corpus (1)

• Partitioning orthogonal polygons into at most 8-vertex pieces, with application to an art gallery theorem