Motivated by fundamental optimization problems in video delivery over wireless networks, we consider the following problem of packing resizable items (PRI). Given is a bin of capacity B > 0, and a set I of items. Each item j ∈ I is of size sj > 0. A packed item must stay in the bin for a fixed time interval. To accommodate more items in the bin, each item j can be compressed to a size pj ∈ [0, ...

Given a set of numbers, and a set of bins of fixed capacity, the NP-complete problem of bin packing is to find the minimum number of bins needed to contain the numbers, such that the sum of the numbers assigned to each bin does not exceed the bin capacity. We present two improvements to our previous bin-completion algorithm. The first speeds up the constant factor per node generation, and the s...

Spatial data sets can be analysed by counting the number of objects in equally sized bins. The bin counts are related to the Pólya urn process, where coloured balls (for example, white or black) are removed from the urn at random. If there are insufficient white or black balls for the prescribed number of trials, the Pólya urn process becomes untenable. In this case, we modify the Pólya urn pro...

It is important to know how the results from a land change model vary based on both the pixel resolution of the maps and the precision of the independent variables because subjective decisions or default values frequently determine these two factors. This paper presents an approach to measure the variation in model accuracy that is triggered by alteration of the pixel resolution and the precisi...

We consider a class of max-profit scheduling problems that occur naturally in many different applications, all involving assignment of jobs to multiple resources under a set of constraints. In the Max-Profit Generalized Assignment Problem (Max-GAP), we are given a set J of m bins (knapsacks), and a set I of n items. Each bin j ∈ J has capacity c(j). Each item i ∈ I has in bin j size `(i, j) and...

A set of items has to be assigned to a set of bins with different sizes. If necessary the size of each bin can be extended. The objective is to minimize the total size, i.e. the sum of the sixs of the bins. In this paper we study both the oll-line case and the on-line variant of this problem under the assumption that each item is smaller than any bin. For the rurmer case, when all times arc kno...

We consider two well-known natural variants of bin packing, and show that these packing problemsadmit asymptotic fully polynomial time approximation schemes (AFPTAS). In bin packing problems,a set of one-dimensional items of size at most 1 is to be assigned (packed) to subsets of sum at most1 (bins). It has been known for a while that the most basic problem admits an AFPTAS. In this...

Considering information entropy (IE), HLA surface expression (SE) regulation phenomenon is considered as information propagation channel with an amount of distortion. HLA gene SE is considered as sink regulated by the inducible transcription factors (TFs) (source). Previous work with a certain number of bin size, IEs for source and receiver is computed and computation of mutual information char...

A novel approach for selecting an appropriate bin size for cell-based diversity assessment is presented. The method measures the sensitivity of the diversity index as a function of grid resolution, using a box-counting algorithm that is reminiscent of those used in fractal analysis. It is shown that the relative variance of the diversity score (sum of squared cell occupancies) of several common...

The 2-dimensional Bin Packing problem is a generalization of the classical Bin Packing problems and is defined as follows: Given a collection of rectangles specified by their width and height, the goal is to pack these into minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions requires a large num...