In this paper, we consider the variable sized bin packing problem where the objective is to minimize the total cost of used bins when the cost of unit size of each bin does not increase as the bin size increases. Two greedy algorithms are described, and analyzed in three special cases: (a) the sizes of items and bins are divisible, respectively, (b) only the sizes of bins are divisible, and (c)...

V.R. Preedy (ed.), Handbook of Anthropometry: Physical Measures of Human Form in Health and Disease, DOI 10.1007/978-1-4419-1788-1_1, © Springer Science+Business Media, LLC 2012 Abstract Sample size estimation is a fundamental step when designing clinical trials and epidemiological studies for which the primary objective is the estimation or the comparison of parameters. One may be interested i...

We consider the two-dimensional bin packing problem (BPP): given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer k ≥ 3 that at most k − 1 bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed k/4-times the bin area. Moreover, ...

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size si ∈ [0, 1] and a color ci ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a ...

We consider three variants of the open-end bin packing problem. Such variants of bin packing allow the total size of items packed into a bin to exceed the capacity of a bin, provided that a removal of the last item assigned to a bin would bring the contents of the bin below the capacity. In the first variant, this last item is the minimum sized item in the bin, that is, each bin must satisfy th...

Standard bin packing is the problem of partitioning a set of items with positive sizes no larger than 1 into a minimum number of subsets (called bins) each having a total size of at most 1. In bin packing games, an item has a positive weight, and given a valid packing or partition of the items, each item has a cost or a payoff associated with it. We study a class of bin packing games where the ...

ID: 18746 Title: FDG-PET Histogram Distances: Novel Predictors of Tumor Response to Chemoradiotherapy Purpose: To examine the accuracy of FGD-PET histogram distances as predictors of pathologic tumor response to chemo-radiotherapy (CRT) in esophageal cancer. Methods: Twenty patients were included. A rigid registration was used to align the post-CRT PET/CT with the pre-CRT PET/CT images. The pri...

We consider the train delivery problem which is a generalization of the bin packing problem and is equivalent to a one dimensional version of the vehicle routing problem with unsplittable demands. The train delivery problem is strongly NP-Hard and does not admit an approximation ratio better than 3/2. We design two types of approximation schemes for the problem. We give an asymptotic polynomial...

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, ...

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...