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Slice and Dice: A Simple, Improved Approximate Tiling Recipe
 In Proceedings of the 13th Annual ACMSIAM Symposium on Discrete Algorithms
, 2002
"... We are given a two dimensional array A[1 \Delta \Delta \Delta n; 1 \Delta \Delta \Delta n] where each A[i; j] stores a nonnegative number. A (rectangular) tiling of A is a collection of rectangular portions A[l \Delta \Delta \Delta r; t \Delta \Delta \Delta b], called tiles, such that no two tiles ..."
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Cited by 6 (2 self)
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We are given a two dimensional array A[1 \Delta \Delta \Delta n; 1 \Delta \Delta \Delta n] where each A[i; j] stores a nonnegative number. A (rectangular) tiling of A is a collection of rectangular portions A[l \Delta \Delta \Delta r; t \Delta \Delta \Delta b], called tiles, such that no two tiles
Multiresolution tiling
 In Proceedings of Graphics Interface ’94
, 1994
"... This paper describes an e cient method for constructing a tiling between a pair of planar contours. The problem is of interest in a number of domains, including medical imaging, biological research and geological reconstructions. Our method, based on ideas from multiresolution analysis and wavelets, ..."
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Cited by 15 (1 self)
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This paper describes an e cient method for constructing a tiling between a pair of planar contours. The problem is of interest in a number of domains, including medical imaging, biological research and geological reconstructions. Our method, based on ideas from multiresolution analysis and wavelets
Improved Approximation Algorithms for Rectangle Tiling and Packing (Extended Abstract)
 Proc. 12th ACMSIAM Symp. on Disc. Alg
, 2001
"... ) 1 Introduction We study several rectangle tiling and packing problems. These are natural combinatorial problems that arise in many applications in databases, parallel computing and image processing. We present new approximation algorithms for these problems. In contrast to the previously known r ..."
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Cited by 17 (3 self)
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) 1 Introduction We study several rectangle tiling and packing problems. These are natural combinatorial problems that arise in many applications in databases, parallel computing and image processing. We present new approximation algorithms for these problems. In contrast to the previously known
Tiling MultiDimensional Arrays
 In Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
, 1999
"... . We continue the study of the tiling problems introduced in [KMP98]. The rst problem we consider is: given a ddimensional array of nonnegative numbers and a tile limit p, partition the array into at most p rectangular, nonoverlapping subarrays, referred to as tiles, in such a way as to minimise ..."
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Cited by 4 (0 self)
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as to minimise the weight of the heaviest tile, where the weight of a tile is the sum of the elements that fall within it. For onedimensional arrays the problem can be solved optimally in polynomial time, where as for twodimensions arrays it is shown in [KMP98] that the problem is NPhard and an approximation
Tiling MultiDimensional Arrays
 In Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
, 1999
"... . We continue the study of the tiling problems introduced in [KMP98]. The rst problem we consider is: given a ddimensional array of nonnegative numbers and a tile limit p, partition the array into at most p rectangular, nonoverlapping subarrays, referred to as tiles, in such a way as to minim ..."
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hard and an approximation algorithm is given. This paper oers a new (d 2 +2d 1)=(2d 1) approximation algorithm for the ddimensional problem (d 2), which improves the (d + 3)=2 approximation algorithm given in [SS99]. In particular, for twodimensional arrays, our approximation ratio is 7=3 improving on the ratio
Function Approximation Using Tile and Kanerva Coding For MultiAgent Systems
"... Function approximation can improve the ability of a reinforcement learner. Tile coding and Kanerva coding are two classical methods for implementing function approximation, but these methods may give poor performance when applied to largescale, highdimensional instances. In the paper, we evaluate ..."
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Cited by 3 (1 self)
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Function approximation can improve the ability of a reinforcement learner. Tile coding and Kanerva coding are two classical methods for implementing function approximation, but these methods may give poor performance when applied to largescale, highdimensional instances. In the paper, we evaluate
Surface Mosaic Synthesis with Irregular Tiles
, 2015
"... Mosaics are widely used for surface decoration to produce appealing visual effects. We present a method for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. Our method employs both continuous optimization and combinatorial ..."
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optimization to improve tile arrangement. In the continuous optimization step, we iteratively partition the base surface into approximate Voronoi regions of the tiles and optimize the positions and orientations of the tiles to achieve a tight fit. Combination optimization performs tile permutation
Alternative Tilings for Improved Surface Area Estimates by Local Counting Algorithms
"... In this paper, we first review local counting methods for perimeter estimation of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting algorithms, can be obtained using hexagonal or triangular grids. We then compa ..."
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Cited by 4 (0 self)
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then compare surface area estimates using local counting techniques for binary threedimensional volumes under the three semiregular polyhedral tilings: the cubic, truncated octahedral, and rhombic dodecahedral tilings. It is shown that for surfaces of random orientation with a uniform distribution
Improved Approximation Algorithms for Rectangle Tiling and Packing P io t r Berman * Bhaskar DasGupta t S. Muthukr i shnan t Suneeta Ramaswami§
"... We provide improved approximation algorithms for several rectangle tiling and packing problems (RTILE, DRTILE and dRPACK) studied in the literature. Our algorithms are highly efficient since their running times are nearlinear in the sparse input size rather than in the domain size. In addition, we ..."
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We provide improved approximation algorithms for several rectangle tiling and packing problems (RTILE, DRTILE and dRPACK) studied in the literature. Our algorithms are highly efficient since their running times are nearlinear in the sparse input size rather than in the domain size. In addition
Noname manuscript No. (will be inserted by the editor) Matrix Recipes for
"... Abstract In this paper, we present and analyze a new set of lowrank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for different configurations to achieve complexity vs. acc ..."
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. accuracy tradeoffs. Moreover, we study acceleration schemes via memorybased techniques and randomized, ɛapproximate matrix projections to decrease the computational costs in the recovery process. For most of the configurations, we present theoretical analysis that guarantees convergence under mild
Results 1  10
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