On Packing Unequal Squares

On Packing Squares with Equal Squares

The following problem arises in connection with certain multidimensional stock cutting problems : How many nonoverlapping open unit squares may be packed into a large square of side a? Of course, if a is a positive integer, it is trivial to see that a2 unit squares can be successfully packed . However, if a is not an integer, the problem becomes much more complicated . Intuitively, one feels th...

On packing squares into a rectangle

We prove that every set of squares with total area 1 can be packed into a rectangle of area at most 2867/2048 = 1.399. . . . This improves on the previous best bound of 1.53. Also, our proof yields a linear time algorithm for finding such a packing.

Translative Packing of Unit Squares into Squares

On-Line Extensible Bin Packing with Unequal Bin Sizes

In the extensible bin packing problem we are asked to pack a set of items into a given number of bins, each with an original size. However, the original bin sizes can be extended if necessary. The goal is to minimize the total size of the bins. We consider the problem with unequal (original) bin sizes and give the complete analysis on a list scheduling algorithm (LS). Namely we present tight bo...

Image Deformation using Moving Least Squares based on Unequal Grids

In this paper, we propose a new method of image deformation. The unequal grids, which are based on the density of edges, were used for the dividing criteria in the MLS (Moving Least Squares) approximation [1] in image deformation. Depending on the importance of the image, we place the size of the grid differently and minimize the distortion that can occur when transforming the image. In this me...