Consider a balls-in-bins process in which each new ball goes into a given bin with probability proportional to f(n), where n is the number of balls currently in the bin and f is a fixed positive function. It is known that these so-called balls-in-bins processes with feedback have a monopolistic regime: if f(x) = x for p > 1, then there is a finite time after which one of the bins will receive a...

The bin packing problem is a well-studied combinatorial NP-hard problem. In the bin packing problem, a sequence of items are packed into bins, the packed items in a bin do not overlap. The objective is to minimize the number of used bins. The size of each item should be no more than the size of a bin. (Zhang, 2011) The algorithms can be divided into two categories: offline algorithm, requiring ...

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, a new type of 3D bin packing problem (BPP) is proposed, in which a number of cuboidshaped items must be put into a bin one by one orthogonally. The objective is to find a way to place these items that can minimize the surface area of the bin. This problem is based on the fact that there is no fixed-sized bin in many real business scenarios and the cost of a bin is proportional to...

We study the 2-dimensional vector packing problem, which is a generalization of the classical bin packing problem where each item has 2 distinct weights and each bin has 2 corresponding capacities. The goal is to group items into minimum number of bins, without violating the bin capacity constraints. We propose an Θ(n)-time approximation algorithm that is inspired by the O(n) algorithm proposed...