On some largest empty orthoconvex polygons in a point set

Abstract

Efficient algorithms for finding some largest empty ortho convex polygons in a point set are presented in this paper. This class of problems are generalizations of the maximum empty rectangle problem. We present simple and efficient algorithms for finding the largest empty ortho convex polygons of the following classes. The algorithm for the L (which is the simplest isothetic polygon after a rectangle) runs in O(n2logn) time in the expected case and O(n3)- time in worst case. The algorithms for the cross shaped polygon, the point visible ortho convex polygon and line visible ortho convex polygon run in O(n3) time. Finally, the algorithm for the edge visible ortho convex polygon runs in O(n2) time.