It has been shown that univalent circle packings lling in the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle packin...

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...

In this paper we study a game problem, called bin packing game with an interest matrix, which is a generalization of all the currently known bin packing games. In this game, there are some items with positive sizes and identical bins with unit capacity as in the classical bin packing problem; additionally we are given an interest matrix with rational entries, whose element aij stands for how mu...

Bin packing is a well known problem which has a large number of applications. Classical bin packing is a simple model where all bins are identical. In the bin packing problem with variable sized bins, we are given a supply of a variety of sizes. This latter model assumes, however, that the cost of a bin is always defined to be its exact size. In this paper we study the more general problem wher...

We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items — we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for unif...

In the Bin Packing Problem with Conflicts (BPPC), we are given a set V = {1, 2, . . . , n} of items, each item i having a non-negative weight wi, and an infinite number of identical bins of weight capacity W . We are also given a conflict graph G = (V,E), where E is a set of edges such that (i, j) ∈ E when i and j are in conflict. Items in conflict cannot be assigned to the same bin. The aim of...

We consider the implementation of an algorithm for the transfer of citrus using an intelligent model for trains, this research is performed based on the problem of packing in containers (Bin Packing), so that objects or boxes should be accommodated in a finite number of cubes considering to minimize the use of containers. The problem of packing containers will be understood and made according t...

This work discusses my attempts to extend Kenyon and Mitzenmacher’s technique for proving diveregnce of the online approximation algorithm Best Fit to Random Fit – another approximation algorithm for the well-known NP-hard problem of bin packing. In specific, the paper goes over Kenyon and Mitzenmacher’s recent advances on divergence of the waste of Best Fit bin packing for the skewed distribut...

The paper deals with multi-dimensional cutting and packing and metaheuristic algorithms. A brief overview of this area is presented, and the general Tabu Search framework of Lodi, Martello and Vigo [LMV99a] is considered in detail. Computational results on multi-dimensional bin packing problems are reported, and possible methods for extending the framework to other packing problems are finally ...

We show a natural graph-theoretic generalization of the Sauer–Shelah lemma. This result is applied to bound the ‘∞ and L1 packing numbers of classes of functions whose range is an arbitrary, totally bounded metric space. ? 1998 Elsevier Science B.V. All rights reserved.