The bin packing optimization problem packs a set of objects into a set of bins so that the amount of wasted space is minimized The bin packing problem has many important applications These include multiprocessor scheduling resource allocation and real world planning packing routing and scheduling optimization problems The bin packing problem is NP complete Since there is therefore little hope i...

A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the numbe...

We consider ensembles of channel codes that are partitioned into bins, and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs. Two main conclusions arise from this analysis: (i) for independent random selection of codewords within a given type class, the random coding exponent of optimal bin...

This whitepaper offers a brief introduction to the BIN system of the Social, Political and Economic Event Database (SPEED) project. BIN provides automatic document categorization of highly nuanced topics across massive-scale document archives. The BIN system allows a group of trained human editors to present the computer with a relatively small collection of hand-categorized documents represent...

Bin packing is a well studied problem involved in many applications. The classical bin packing problem is about minimising the number of bins and ignores how the bins are utilised. We focus in this paper, on a variant of bin packing that is at the heart of efficient management of data centres. In this context, servers can be viewed as bins and virtual machines as items. The efficient management...

The three-dimensional bin packing problem is a practical problem faced in modern industrial processes such as container ship loading, pallet loading, plane cargo management, and warehouse management. This article considers a three-dimensional bin packing problem in which objects of various volumes are packed into a single bin to maximize the number of objects packed. The bin packing problem ini...

Imagine that there are two bins to which balls are added sequentially, and each incoming ball joins a bin with probability proportional to the pth power of the number of balls already there. A general result says that if p > 1/2, there almost surely is some bin that will have more balls than the other at all large enough times, a property that we call eventual leadership. In this paper, we comp...