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 non-negative 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

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

) 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

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 one-dimensional arrays the problem can be solved optimally in polynomial time, where as for two-dimensions arrays it is shown in [KMP98] that the problem is NP-hard and an approximation

-hard and an approximation algorithm is given. This paper oers a new (d 2 +2d 1)=(2d 1) approximation algorithm for the d-dimensional problem (d 2), which improves the (d + 3)=2 approximation algorithm given in [SS99]. In particular, for two-dimensional arrays, our approximation ratio is 7=3 improving on the ratio

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 large-scale, high-dimensional instances. In the paper, we evaluate

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

then compare surface area estimates using local counting techniques for binary three-dimensional volumes under the three semi-regular polyhedral tilings: the cubic, truncated octahedral, and rhombic dodecahedral tilings. It is shown that for surfaces of random orientation with a uniform distribution

We provide improved approximation algorithms for several rectangle tiling and packing problems (RTILE, DRTILE and d-RPACK) studied in the literature. Our algorithms are highly efficient since their running times are near-linear in the sparse input size rather than in the domain size. In addition

. accuracy tradeoffs. Moreover, we study acceleration schemes via memory-based techniques and randomized, ɛ-approximate 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