Computing the largest empty rectangle
SIAM Journal on Computing
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
Searching for empty convex polygons
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient algorithms for identifying all maximal isothetic empty rectangles in VLSI layout design
FST and TC 10 Proceedings of the tenth conference on Foundations of software technology and theoretical computer science
Finding the largest area axis-parallel rectangle in a polygon
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Location of the Largest Empty Rectangle among Arbitrary Obstacles
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
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Pattern Recognition and Image Analysis
Empty pseudo-triangles in point sets
Discrete Applied Mathematics
Submatrix maximum queries in Monge matrices and Monge partial matrices, and their applications
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Largest inscribed rectangles in convex polygons
Journal of Discrete Algorithms
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This work generalizes the classical problem of finding the largest empty rectangle among obstacles in 2D. Given a set P of n points, here a maximal empty rectangle (MER) is defined as a rectangle of arbitrary orientation such that each of its four boundaries contain at least one member of P and the interior of the rectangle is empty. We propose a very simple algorithm based on standard data structure to locate a MER of largest area in the plane. The worst-case time complexity of our algorithm is O(n3). Though the worst-case space complexity is O(n2), it reserves O(n log n) space on an average to maintain the required data structure during the execution of the algorithm.