Guarding Art Galleries by Guarding Witnesses

  title={Guarding Art Galleries by Guarding Witnesses},
  author={Kyung-Yong Chwa and Byung-Cheol Jo and Christian Knauer and Esther Moet and Ren{\'e} van Oostrum and Chan-Su Shin},
Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the boundary of P , and there can be at most one witness per edge. We give an algorithm to compute a minimal witness set for P in O(n log n) time… CONTINUE READING