In the bin covering problem there is a group L=(a1; : : : ; an) of items with sizes s̃(ai)∈ (0; 1), and the goal is to 6nd a packing of the items into bins to maximize the number of bins that receive items of total size at least 1. This is a dual problem to the classical bin packing problem. In this paper we present the 6rst asymptotic fully polynomial-time approximation scheme for the problem. ...

In this paper we study the Variable Size Bin Packing Problem (VSBPP) which is a generalization of the Bin Packing Problem where bins of different capacities (and different costs) are available for packing a set of items. The objective is to pack all the items minimizing the total cost associated with the bins. We discuss applications of the VSBPP and propose and discuss one generic (non-linear ...

A numerical model BAEROSOL for solving the general dynamic equation (GDE) of aerosols is presented. The goal was to model the capture of volatilized metals by sorbents under incinerator-like conditions. The model is based on algorithms presented by Jacobson and Turco [Aerosol Science and Technology 22 (1995) 73]. A hybrid size bin was used to model growth and formation of particles from the con...

The time histogram is a fundamental tool for representing the inhomogeneous density of event occurrences such as neuronal firings. The shape of a histogram critically depends on the size of the bins that partition the time axis. In most neurophysiological studies, however, researchers have arbitrarily selected the bin size when analyzing fluctuations in neuronal activity. A rigorous method for ...

Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails to distinguish between most algorithms of interest; all “reasonable” algorithms have a competitive ratio of 1 2 . Thus, in order to get a better understandin...

In this paper, we consider the Generalized Bin Covering problem: We are given m bin types, where each bin of type i has profit pi and demand di. Furthermore, there are n items, where item j has size sj . A bin of type i is covered if the set of items assigned to it has total size at least the demand di. In that case, the profit of pi is earned and the objective is to maximize the total profit. ...

We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly environment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size B ∈ N. The packing process is subject to the constraint that at any moment in time at most q ∈ N bins are partiall...

The rapid growth of Internet brings the need for a low cost high performance file system. Two objectives are to be pursued in building such a large scale storage system on multiple disks: load balancing and storage minimization. We investigate the optimization problem of placing variable-size data items onto multiple disks with replication to achieve the two objectives. An approximate algorithm...

In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90◦-rotation is allowed. 1-space bounded means there is only one “active” bin. If the “active” bin cannot acco...

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. FirstFit algorithm packs each item into the first bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that the a...