On the rectangle escape problem

On the Rectangle Escape Problem

Motivated by a bus routing application, we study the following rectangle escape problem: Given a set S of n rectangles inside a rectangular region R, extend each rectangle in S toward one of the four borders of R so that the maximum density over the region R is minimized, where the density of each point p ∈ R is defined as the number of extended rectangles containing p. We show that the problem...

On the d-Runaway Rectangle Escape Problem

In the Rectangle Escape problem, we are given a set of rectangles S in a rectangular region R, and we would like to extend these rectangles to one of the four sides of R while ensuring that the maximum number of overlaps is minimized. More formally, define the density of a point p in R as the number of extended rectangles that contain p. The question is then to find an extension with the smalle...

The Runaway Rectangle Escape Problem

Motivated by the applications of routing in PCB buses, the Rectangle Escape Problem was recently introduced and studied. In this problem, we are given a set of rectangles S in a rectangular region R, and we would like to extend these rectangles to one of the four sides of R. Define the density of a point p in R as the number of extended rectangles that contain p. The question is then to find an...

On the maximum empty rectangle problem

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...

On the narrow escape problem