Geometric applications of a matrix searching algorithm
SCG '86 Proceedings of the second annual symposium on Computational geometry
Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Fining k points with minimum spanning trees and related problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Parallel searching in generalized Monge arrays with applications
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Superlinear bounds on matrix searching
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Computers
Optimal parallel algorithms for direct dominance problems
Nordic Journal of Computing
Largest Empty Rectangle among a Point Set
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Largest empty rectangle among a point set
Journal of Algorithms
On finding an empty staircase polygon of largest area (width) in a planar point-set
Computational Geometry: Theory and Applications
An efficient algorithm for finding empty space for online FPGA placement
Proceedings of the 41st annual Design Automation Conference
Fast algorithms for finding disjoint subsequences with extremal densities
Pattern Recognition
On the density and discrepancy of a 2D point set with applications to thermal analysis of VLSI chips
Information Processing Letters
Computing a largest empty arbitrary oriented rectangle: theory and implementation
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Recognition of largest empty orthoconvex polygon in a point set
Information Processing Letters
Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media
ACM SIGGRAPH Asia 2010 papers
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
The mono- and bichromatic empty rectangle and square problems in all dimensions
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Fast algorithms for finding disjoint subsequences with extremal densities
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Hardness of discrepancy computation and ε-net verification in high dimension
Journal of Complexity
The class cover problem with boxes
Computational Geometry: Theory and Applications
An optimal algorithm for rectangle placement
Operations Research Letters
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
An in-place min-max priority search tree
Computational Geometry: Theory and Applications
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We provide two algorithms for solving the following problem: Given a rectangle containing n points, compute the largest-area and the largest-perimeter subrectangles with sides parallel to the given rectangle that lie within this rectangle and that do not contain any points in their interior. For finding the largest-area empty rectangle, the first algorithm takes &Ogr;(n log3 n) time and &Ogr;(n) memory space and it simplifies the algorithm given by Chazelle, Drysdale and Lee which takes &Ogr;(n log3 n) time but &Ogr;(n log n) storage. The second algorithm for computing the largest-area empty rectangle is more complicated but it only takes &Ogr;(n log2 n) time and &Ogr;(n) memory space. The two algorithms for computing the largest-area rectangle can be modified to compute the largest-perimeter rectangle in &Ogr;(n log2 n) and &Ogr;(n log n) time, respectively. Since &OHgr;(n log n) is a lower bound on time for computing the largest-perimeter empty rectangle, the second algorithm for computing such a rectangle is optimal within a multiplicative constant.