On the maximum empty rectangle problem
TLDR
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.About:
This article is published in Discrete Applied Mathematics.The article was published on 1984-07-01 and is currently open access. It has received 111 citations till now. The article focuses on the topics: Largest empty rectangle & Rectangle method.read more
Citations
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Book ChapterDOI
Maximal Empty Boxes Amidst Random Points
Adrian Dumitrescu,Minghui Jiang +1 more
TL;DR: It is shown that the expected number of maximal empty axis-parallel boxes amidst n random points in the unit hypercube [0,1] d in ℝ d is 1, where d is fixed, and the first valid proof for the Θ(n log d − 1 n) bound is presented.
Posted Content
Perfect vector sets, properly overlapping partitions, and largest empty box.
Adrian Dumitrescu,Minghui Jiang +1 more
TL;DR: An algorithm is presented that finds a large empty box amidst $n$ points in $[0,1]^d$: a box whose volume is at least $\frac{d}}{4(n + \log{d})}$ can be computed in $O(n+d d)$ time.
Proceedings Article
Space-efficient Algorithms for Empty Space Recognition among a Point Set in 2D and 3D.
Minati De,Subhas C. Nandy +1 more
TL;DR: This paper considers the problem of designing in-place algorithms for computing the maximum area empty rectangle of arbitrary orientation among a set of points in 2D, and the maximum volume empty axisparallel cuboid among aSet of Points in 3D.
Journal ArticleDOI
The largest empty rectangle containing only a query object in Spatial Databases
TL;DR: This paper presents several algorithms for finding the empty rectangle in R with the largest area, sides parallel to the axes of the space, and containing only a query point q, and provides formal proofs of the correctness of these algorithms.
Journal ArticleDOI
Global cutting for the maximum rectangular block from arbitrary closed region
Chi-Cheng Cheng,Jen-Shen Tsai +1 more
TL;DR: In this paper, the authors used adaptive thresholding, component labeling, and 8-neighbor connectivity to develop the profile of the region and then determined the maximum rectangular block (MRB) from the remaining closed space.
References
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Journal ArticleDOI
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
TL;DR: A mmmaal spammuag tree for P can be derived from a Voronot diagram for P m hnear tmae by using prewously known results.
Journal ArticleDOI
Voronoi Diagrams in L1 (L∞) Metrics with 2-Dimensional Storage Applications
Der-Tsai Lee,C. K. Wong +1 more
TL;DR: It is shown in this paper that there exists a natural isometry between the L_1 and L_\infty metrics, which implies the existence of a polynomial time algorithm for the OPP in one metric and the existence for the same problem in the other metric.
Generalization of heaps and its applications
TL;DR: A data structure called "generalized heap," which is designed primarily to maintain the solutions of a certain group of problems while the data set is changing over time, is introduced.