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A new algorithm for the largest empty rectangle problem

Abstract

A rectangleA and a setS ofn points inA are given. We present a new simple algorithm for the so-called largest empty rectangle problem, i.e., the problem of finding a maximum area rectangle contained inA and not containing any point ofS in its interior. The computational complexity of the presented algorithm isO(n logn + s), where s is the number of possible restricted rectangles considered. Moreover, the expected performance isO(n · logn).

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Communicated by D. T. Lee.

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Orlowski, M. A new algorithm for the largest empty rectangle problem. Algorithmica 5, 65–73 (1990). https://doi.org/10.1007/BF01840377

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Key words

  • Computational geometry
  • Algorithms
  • Computational complexity
  • Largest empty rectangle problem