Efficient algorithms for identifying all maximal isothetic empty rectangles in VLSI layout design

  • Subhas C Nandy
  • Bhargab B Bhattacharya
  • Sibabrata Ray
Geometric Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 472)


In this paper, we consider the following problem of computational geometry which has direct applications to VLSI layout design : given a set of n isothetic solid rectangles on a rectangular floor, identify all maximal-empty-rectangles (MER's). A tighter upper bound on the number of MER's is derived. A new algorithm based on interval trees for identifying all MER's is then presented which runs in O(nlogn+R) time in the worst case and in O(nlogn) time in the average case, where R denotes the number of MER's. The space complexity of the algorithm is O(n). Finally, we explore the problem of recognizing the maximum (area)- empty- rectangle without explicitly generating all MER's. Our analysis shows that, on an average, around 70% of MER's need not be examined in order to locate the maximum. The proposed algorithm can readily be tailored to solve the MER problem in an ensemble of points as well as within an isothetic polygon.


Computational geometry VLSI layout placement geometric algorithms complexity interval trees 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Subhas C Nandy
    • 1
  • Bhargab B Bhattacharya
    • 1
  • Sibabrata Ray
    • 1
  1. 1.Electronics UnitIndian Statistical InstituteCalcuttaIndia

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