Given a rectangle A and a set S of n points in A, the maximum empty rectangle problem is that of finding a largest-area rectangle which is contained in A. has its sides parallel to Ihose ofA. and does Dot contain any of the points in S. This Dote describes an efficient algorithm for solving this problem.

Saving a patients live in an emergency state especially if he is far from medical institutions, is considered to be the primary concern of the physician. With a mobile physician, patients health state may vary to be in a critical situation that requires immediate medical intervention. Having chosen the medical institution as destination, the doctor must react immediately and reach his patient a...

Given a rectangle A and a set S of n points in A, we consider the problem, called the maximum empty rectangle problem, of finding a maximum area rectangle that is fully contained in A and does not contain any point of S in its interior. An O(n’) time algorithm is presented. Furthermore, it is shown that if the points of S are drawn randomly and independently from A, the problem can be solved in...

The largest empty circle (LEC) problem is defined on a set P and consists of finding the largest circle that contains no points in P and is also centered inside the convex hull of P . The LEC is always centered at either a vertex on the Voronoi diagram for P or on an intersection between a Voronoi edge and the convex hull of P . Thus, finding the LEC consists of constructing a Voronoi diagram a...