Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Near real-time shadow generation using BSP trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
On maximum flows in polyhedral domains
Journal of Computer and System Sciences
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
On the optimal binary plane partition for sets of isothetic rectangles
Information Processing Letters
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Histogram-based estimation techniques in database systems
Histogram-based estimation techniques in database systems
Surface approximation and geometric partitions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Rectangular tiling in multi-dimensional arrays
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STHoles: a multidimensional workload-aware histogram
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Introduction to VLSI Systems
New Results on Binary Space Partitions in the Plane (Extended Abstract)
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Binary Space Partitions for Sets of Hyperrectangles
ACSC '95 Proceedings of the 1995 Asian Computing Science Conference on Algorithms, Concurrency and Knowledge
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Linear Size Binary Space Partitions for Fat Objects
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Mining Deviants in a Time Series Database
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications
On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications
Binary space partitions for fat rectangles
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Binary space partitions for 3D subdivisions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Optimal Genome Tiling with Applications to Microarray Design and Homology Search
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Geometric algorithms for optimal airspace design and air traffic controller workload balancing
Journal of Experimental Algorithmics (JEA)
Approximating Points by a Piecewise Linear Function: I
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation algorithms for min-max generalization problems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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We are given a two dimensional array A[1 ⋅⋅⋅ n, 1 ⋅⋅⋅ n] where each A[i, j] stores a non-negative number. A (rectangular) tiling of A is a collection of rectangular portions A[l ⋅⋅⋅ r, t ⋅⋅⋅ b], called tiles, such that no two tiles overlap and each entry A[i, j] is contained in a tile. The weight of a tile is the sum of all array entries in it.In the MAX-MIN problem, we are given a weight bound W and our goal is to find a tiling such that (a) each tile is of weight at least W (the MIN condition) and (b) the number of tiles is maximized (the MAX condition). In the MIN-MAX problem, we are given a weight bound W again and our goal is to find a tiling such that (a) each tile has weight at most W and (b) the number of tiles is minimized. These two basic problems have many variations depending on the weight functions, whether some areas of A must not be covered, or whether some portion of A may be discarded, etc. These problems are not only natural combinatorial problems, but also arise in a plethora of applications, e.g., in databases and data mining, video compression, load balancing, building index structures, manufacturing and so forth.Both the above tiling problems (as well as all of their variations relevant to this paper) are known to be NP-hard. In this paper, we present approximations algorithms for solving these problems based on epicurean methods : variations of a basic slice-and-dice technique. Surprisingly, these simple algorithms yield small constant factor approximations for all these problems. For some of the problems, our results are the first known approximations; for others, our results improve the known algorithms significantly in approximation bounds and/or running time. Of independent interest are the tight bounds we show for sizes of the binary space partition trees for isothetic rectangles.