Art gallery problem - Printable Version +- MKLab (https://mklab.gr) +-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1) +--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3) +---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13) +---- Thread: Art gallery problem (/showthread.php?tid=545)

Art gallery problem - mklabgr - 06-21-2026 Art gallery problem Summary The Art Gallery Problem is a classic problem in computational geometry that asks: What is the minimum number of guards needed to observe every point inside an art gallery? The gallery is modeled as a simple polygon, and a guard can see any point connected to it by a line segment that remains inside the polygon. A fundamental result, known as Chvátal’s Art Gallery Theorem, states that any simple polygon with n vertices can always be fully guarded by at most $⌊n/3⌋$ guards, and that this bound is sometimes necessary.  The problem has inspired numerous variations, including restrictions on where guards may be placed and extensions to three-dimensional spaces, and it has applications in robotics, computer vision, wireless network coverage, surveillance, and stage lighting. Determining the minimum number of guards for a given polygon is computationally difficult and remains an important topic in geometry and algorithm design.  ARTICLE