For bin packing, the input consists of n items with sizes s1, . . . , sn ∈ [0,1] which have to be assigned to aminimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed techniques from discrepancy theory to find a solution using at mostOPT +O(logOPT · log logOPT ) bins. In this paper, we present an approximation algorithm that has an ...

Abstract Insect infestations can result in a damaged or destroyed product, costing producers and retailers millions of dollars annually. Postharvest insects move through space searching for mates, food, shelter. Movement sanitation activities, insecticide applications also drive their spatial distribution patterns. Determining distributions population density provides important information to d...

In variable sized bin packing, a number of bin types are given and the goal is to pack a list of items by choosing appropriate bins such that the total size of bins used is minimized. In this paper, we present absolute worst-case analysis for on-line algorithms. Then we consider an related problem: how to design k different bin sizes such that for any item list the waste space of bins used is m...

The bin-packing problem (BPP) and its multi-dimensional variants have many practical applications, such as packing objects in boxes, production planning, multiprocessor scheduling, etc. The classical singleobjective formulation of the two-dimensional bin packing (2D-BPP) consists of packing a set of objects (pieces) in the minimum number of bins (containers). This paper presents a new Pareto-ba...

A large set of rising adiabatic parcel simulations is executed to investigate the combined diffusional and accretional growth of cloud droplets in maritime and continental conditions, and to assess the impact of enhanced droplet collisions due to small-scale cloud turbulence. The microphysical model applies the droplet number density function to represent spectral evolution of cloud and rain/dr...

The main contribution of this paper is an optimal bounded space online algorithm for variable-sized multidimensional packing. In this problem, hyperboxes must be packed in ddimensional bins of various sizes, and the goal is to minimize the total volume of the used bins. We show that the method used can also be extended to deal with the problem of resource augmented multidimensional packing, whe...

Local Binary Patterns (LBP) have been well exploited for facial image analysis recently. In the existing work, the LBP histograms are extracted from local facial regions, and used as a whole for the regional description. However, not all bins in the LBP histogram are necessary to be useful for facial representation. In this paper, we propose to learn discriminative LBP-Histogram (LBPH) bins for...

As Bin Packing is NP-hard already for k = 2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the items are polynomially bounded integers, then the problem can be solved in time n for an input of length n by dynamic programming. We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in u...

We consider the Variable Size Bin Packing Problem with Fixed Costs, a generalization of the well-known bin packing problem where a set of items must be packed within a set of heterogeneous bins characterized by possibly different volumes and fixed costs. The objective of the problem is to select the bins to pack all items while minimizing the total cost incurred for the selected bins. We presen...

We study a higher-dimensional ‘balls-into-bins’ problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this pap...