Efficient algorithms for Identifying All Maximal Isothetic Empty Rectangles in VLSI Layout Design

  title={Efficient algorithms for Identifying All Maximal Isothetic Empty Rectangles in VLSI Layout Design},
  author={Subhas C. Nandy and Bhargab B. Bhattacharya and S. Ray},
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… 

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  • 1976
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