Motivated by the problem of packing Virtual Machines on physical servers in the cloud, we study the problem of one-dimensional online stochastic bin packing. Items with sizes sampled independent and identically (i.i.d.) from a distribution with integral support arrive as a stream and must be packed on arrival in bins of size B, also an integer. The size of an item is known when it arrives and t...

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin’s level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst...

The two-dimensional discrete bin-packing problem (2BP ) consists in minimizing the number of identical rectangles used to pack a set of smaller rectangles. This problem is NP-hard. It occurs in industry if pieces of steel, wood, or paper have to be cut from larger rectangles. It belongs to the family of cutting and packing problems, more precisely to the class of TwoDimensional Single Bin Size ...

In the bin covering problem we are asked to pack a list X(n) = (x1, x2, . ,x,) of n items, each with size no larger than one, into the maximum number of bins such that the sum of the sizes of the items in each bin is at least one. In this article we analyze the asymptotic average-case behavior of the Iterated-Lowest-Fit-Decreasing (IUD) algorithm proposed by Assmann et al. Let OPT(X(n)) denote ...

We tested associative-based accounts of orientation by investigating the influence of environment size on the use of feature and geometric cues for reorientation. Two groups of participants were trained in dynamic three-dimensional virtual rectangular environments that differed in size to find a distinctly colored bin located at one of the four corners. Subsequently, we probed the reliance on f...

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems — including multi-constraint variants — by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. Our formul...

The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack set items. There are many real-life applications VCSBPP where focus improve efficiency solution method. In spite existence fuzzy approaches adapt other optimization problems real life conditions, has not been extensively studied terms relaxations crisp...

Bin and bulk schemes are the two primary methods to parameterize cloud microphysical processes. This study attempts reveal how their structural differences (size-resolved vs. moment-resolved) manifest in terms of precipitation properties. We use a scheme, Arbitrary Moment Predictor (AMP), which uses process parameterizations identical those bin scheme but predicts only moments size distribution...

The multi-particle Bose-Einstein correlations are the source of "intermittency" in high energy hadronic collisions. The power-law like increase of factorial moments with decreasing bin size was obtained by complete event weighing technique with gaussian approximation of space-time particle emitting source shape. The value of source size parameter was found to be higher than the common one tted ...

In the paper ” Relations between capacity utilization and minimal bin number“[HS12] the following two-dimensional bin packing problem (BPP) is considered: given a set K of rectangular items of sizes li × wi and bins of size L×W . Rotation of the items is not permitted. It is shown, if every item fits into the given bin and if the total area of the items does not exceed the area of the bin then ...