Computational Geometry Column 60

This column is devoted to maximal empty axis-parallel rectangles amidst a point set. In particular, among these, maximum-area rectangles are of interest.

[1]  D. T. Lee,et al.  On the maximum empty rectangle problem , 1984, Discret. Appl. Math..

[2]  J. Mark Keil,et al.  The Mono- and Bichromatic Empty Rectangle and Square Problems in All Dimensions , 2010, LATIN.

[3]  J. Halton On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[4]  Bernard Chazelle,et al.  The discrepancy method - randomness and complexity , 2000 .

[5]  Dániel Marx,et al.  Parameterized Complexity and Approximation Algorithms , 2008, Comput. J..

[6]  Amitava Datta,et al.  An efficient algorithm for computing the maximum empty rectangle in three dimensions , 2000, Inf. Sci..

[7]  Haim Kaplan,et al.  Submatrix maximum queries in Monge matrices and Monge partial matrices, and their applications , 2012, SODA.

[8]  J. Hammersley MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[9]  Haim Kaplan,et al.  Efficient Colored Orthogonal Range Counting , 2008, SIAM J. Comput..

[10]  Alok Aggarwal,et al.  Fast algorithms for computing the largest empty rectangle , 1987, SCG '87.

[11]  G. Rote,et al.  Quasi-Monte-Carlo methods and the dispersion of point sequences , 1996 .

[12]  Murray S. Klamkin Unsolved Problems in Intuitive Mathematics, Vol. II, Unsolved Problems in Geometry (H. T. Croft, K. J. Falconer, and R. K Guy) , 1992, SIAM Rev..

[13]  H. T. Kung,et al.  On the Average Number of Maxima in a Set of Vectors and Applications , 1978, JACM.

[14]  J. Matousek,et al.  Geometric Discrepancy: An Illustrated Guide , 2009 .

[15]  Peter Winkler Puzzled: Rectangles galore , 2010 .

[16]  J. Mark Keil,et al.  The Bichromatic Rectangle Problem in High Dimensions , 2009, CCCG.

[17]  Renée J. Miller,et al.  Mining for empty spaces in large data sets , 2003, Theor. Comput. Sci..

[18]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[19]  John Augustine,et al.  Querying for the Largest Empty Geometric Object in a Desired Location , 2010, 1004.0558.

[20]  Magnus Wahlström,et al.  Hardness of discrepancy computation and ε-net verification in high dimension , 2012, J. Complex..

[21]  Rolf Klein,et al.  Direct dominance of points , 1986 .

[22]  Peter Winkler PuzzledSolutions and sources , 2008, CACM.

[23]  Adrian Dumitrescu,et al.  Maximal Empty Boxes Amidst Random Points , 2013, Comb. Probab. Comput..

[24]  Csaba D. Tóth,et al.  Packing anchored rectangles , 2015, Comb..

[25]  Adrian Dumitrescu,et al.  On the Largest Empty Axis-Parallel Box Amidst n Points , 2009, Algorithmica.