The complexity of manipulating hierarchically defined sets of rectangles
Abstract
Algorithms that manipulate sets of rectangles are of great practical importance in VLSI design systems and other applications. Although much theoretical work has appeared recently on the complexity of rectangle problems, it has assumed that the inputs are given as a list of rectangles. In this paper we study the complexity of rectangle problems when the inputs are given in a hierarchical language that allows the designer to build large designs by replicating small designs. We will see that while most of the problems are NPhard in the general case, there are O(N lg N) algorithms that process inputs obeying certain restrictions.
 Publication:

Interim Report CarnegieMellon Univ
 Pub Date:
 April 1981
 Bibcode:
 1981cmu..rept.....B
 Keywords:

 Computer Aided Design;
 Data Management;
 Integrated Circuits;
 Large Scale Integration;
 Rectangles;
 Algorithms;
 Computer Graphics;
 Exponential Functions;
 Hierarchies;
 Mathematical Models;
 Electronics and Electrical Engineering