In order to verify and test the performance of new packing algorithms relative to existing algorithms, test problems are needed. The scope of published test instances for 2D rectangular and irregular packing has been fairly limited in terms of object size, number and dimension of items. A systematic investigation into the performance of new algorithms requires the use of a range of test problem...

Let X = {X(t), t ∈ R+} be an operator stable Lévy process in R with exponent B, where B is an invertible linear operator on R. We determine the Hausdorff dimension and the packing dimension of the range X([0, 1]) in terms of the real parts of the eigenvalues of B. Running Title Dimension of Operator Stable Lévy Processes

This paper deals with the densest packing of equal circles in a square problem. Sharp bounds for the density of optimal circle packings have given. Several known optimal and approximate circle packings contain optimal substructures. Based on this observation it is sometimes easy to determine the minimal polynomials of the arrangements.

We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assume the Hausdorff functions are continuous or blanketed, and we do not assume the metric space is a subset of Euclidean space. We discuss the covering measure (= centered Hausdorff measure) and packing...

We study the following variant of the bin packing problem. We are given a set of items, where each item has a (non-negative) size and a color. We are also given an integer parameter k, and the goal is to partition the items into a minimum number of subsets such that for each subset S in the solution, the total size of the items in S is at most 1 (as in the classical bin packing problem) and the...

We study the online bin packing problem, in which a list of items with integral size between 1 to B arrives one at a time. Each item must be assigned in a bin of capacity B upon its arrival without any information on the next items, and the goal is to minimize the number of used bins. We present an asymptotic competitive scheme, i.e., for any > 0, the asymptotic competitive ratio is at most ρ∗ ...