The two-dimensional strip packing is a special case of “Cutting and Packing” problems that arises in many applications. The problem seeks to pack a given set of rectangles into a strip of given width in order to minimize its length. Some applications in which the strip packing problem arises are: Cutting pieces from wooden boards, cutting pieces from glass or steel sheets, optimal layout of ind...

This paper reviews two and three-dimensional packing problems and their solution utilising genetic algorithms. The dimensions and the geometry of the figures involved in the allocation process classify packing problems. Since the genetic representation of the problem is vital to the performance of the genetic algorithm, particular emphasis is put on the techniques used for the representation of...

The MPI Standard supports derived datatypes, which allow users to describe noncontiguous memory layout and communicate noncontiguous data with a single communication function. This feature enables an MPI implementation to optimize the transfer of noncontiguous data. In practice, however, few MPI implementations implement derived datatypes in a way that performs better than what the user can ach...

The problem of bin packing with arbitrary conflicts was introduced in [3]. In this paper, we consider a restricted problem, bin packing with clique-graph conflicts. We prove bounds for several approximation algorithms, and show that certain onand off-line algorithms are equivalent. Finally, we present an optimal polynomial-time algorithm for the case of constant item sizes, and analyze its perf...

The fractal dimension of the Apollonian sphere packing has been computed numerically up to six trusty decimal digits. Based on the 31 944 875 541 924 spheres of radius greater than 2-19 contained in the Apollonian packing of the unit sphere, we obtained an estimate of 2.4739465, where the last digit is questionable. Two fundamentally different algorithms have been employed. Outlines of both alg...

We present approximation algorithms for the twoand three-dimensional bin packing problems and the three-dimensional strip packing problem. We consider the special case of these problems in which a parameter (a positive integer) is given, indicating that each of the dimensions of the items to be packed is at most of the corresponding dimension of the recipient. We analyze the asymptotic performa...

Rectangle-packing problem involves many industrial applications. For example, in shipping industry, various size boxes have to be loaded as many as possible in a larger container. In wood or glass industries, rectangular components have to be cut from large sheets of material. In very large scale integration (VLSI) floor planning, various chips have to be laid on the chip board, and so on. The ...

This paper presents the use of genetic algorithms (GA) for solving the dual bin packing problem using fuzzy objectives. In bin packing problems, a list, L of items is to be packed into a minimum number of bins. In dual bin packing the items are packed into a maximum number of bins, assuring a minimum weight for each bin. We consider a class which we call dynamic dual bin packingg. Similar to th...

The bin-packing problem asks for a packing of a list of items of sizes from (0; 1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two e6cient on-line algorithms for this problem. We show that, for increasing values of k, the bound on the asymptotic worst-ca...

We present approximation algorithms for the three-dimensional strip packing problem, and the three-dimensional bin packing problem. We consider orthogonal packings where ninety-degree rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 2.64, and 4.89, respectively. These algorithms are for the more general case in which the bounded dimensions of t...