We consider the twoand three-dimensional strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the two-dimensional SPP, which improves the packing of the well-known FFDH-heuristic and state theoretical results of this algorithm. Furthermore, we prove new upp...

1-d bin packing and 2-d bin packing are classic NP-complete problems that are motivated by industrial applications of stock cutting, data storage, etc. In this paper, we look at a slightly more general problem that is primarily motivated by VLSI design. In VLSI design, one wants to pack a given number of rectangles (which might be RAM chips, transistors, etc.) into a wafer of minimum area to re...

Given a set of rectangles and a rectangular container with a fixed width, called a strip, the twodimensional strip packing problem (2SP) requires all the given rectangles to be placed orthogonally without overlap within the strip so as to minimize the height of the strip. 2SP and its variants have many applications in steel and textile industries, and it has indirect application in scheduling p...

In this paper, we study the 3D strip packing problem in which we are given a list of 3dimensional boxes and required to pack all of them into a 3-dimensional strip with length 1 and width 1 and unlimited height to minimize the height used. Our results are below: i) we give an approximation algorithm with asymptotic worst-case ratio 1.69103, which improves the previous best bound of 2 + ǫ by Jan...