Journal Article10.1007/BF01840377
A new algorithm for the largest empty rectangle problem
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TL;DR: 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, is presented.
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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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References
On the maximum empty rectangle problem
TL;DR: In this article, the authors considered the problem of finding a maximum area rectangle that is fully contained in a given rectangle A and does not contain any point of S in its interior.
119
Computing the Largest Empty Rectangle
Bernard Chazelle,Robert L. Scot Drysdale,Der-Tsai Lee +2 more
- 11 Apr 1984
TL;DR: A divide-and-conquer approach similar to the ones used by Strong and Bentley is used and a new notion of Voronoi diagram is introduced along with a method for efficient computation of certain functions over paths of a tree.
A note on finding a maximum empty rectangle
TL;DR: This note describes an efficient algorithm for solving the maximum empty rectangle problem, which is that of finding a largest-area rectangle which is contained in A, has its sides parallel to those of A, and does not contain any of the points in S.
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Computing the largest empty rectangle
TL;DR: A divide-and-conquer approach similar to the ones used by Bentley is used and a new notion of Voronoi diagram is introduced along with a method for efficient computation of certain functions over paths of a tree.
•Journal Article
On Maximum Empty Rectangle Problem
A. Naamad,W.L.Hsu,Der-Tsai Lee +2 more
TL;DR: It is shown that if the points of S are drawn randomly and independently from A , the problem can be solved in O( n (log n ) 2 ) expected time.
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