The complexity of manipulating hierarchically defined sets of rectangles

  • Jon Louis Bentley
  • Thomas Ottmann
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 118)


Algorithms that manipulate sets of rectangles are of rectangles are of great practical importance in VLST 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 NP-hard in the general case, there are O(N log N) algorithms that process inputs obeying certain restrictions.


VLSI Design Query Object Hierarchical Design Symbol Number Consistent Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Jon Louis Bentley
    • 1
  • Thomas Ottmann
    • 2
  1. 1.Department of Computer Science and MathematicsCarnegie-Mellon-UniversityPittsburghU.S.A.
  2. 2.Institut für Angewandte Informatik und Formale BeschreibungsverfahrenUniversität KarlsruheKarlsruhe 1West-Germany

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