Particle filters are key algorithms for object tracking under non-linear, non-Gaussian dynamics. The high computational cost of particle filters, however, hampers their applicability in cases where the likelihood model is costly to evaluate, or where large numbers of particles are required to represent the posterior. We introduce the piecewise constant sequential importance sampling/resampling ...

We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly environment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size B ∈ N. The packing process is subject to the constraint that at any moment in time at most q ∈ N bins are partiall...

Event-to-event fluctuations of the spatial patterns of the final states of high-enery collisions, referred to as erraticity, are studied for the data generated by a soft-interaction model called ECOMB. The moments Cp,q do not show simple power-law dependences on the bin size. New measures of erraticity are proposed that generalizes the bin-size dependence. The method should be applied not only ...

The bin packing problem (BP) consists in finding the minimum number of bins necessary to pack a set of items so that the total size of the items in each bin does not exceed the bin capacity C. The bin capacity is common for all the bins. This problem can be solved in Constraint Programming (CP) by introducing one placement variable xi for each item and one load variable lj for each bin. The Pac...

We consider the Variable Cost and Size Bin Packing Problem, a generalization of the well-known bin packing problem, where a set of items must be packed into a set of heterogeneous bins characterized by possibly different volumes and fixed selection costs. The objective of the problem is to select bins to pack all items at minimum total binselection cost. The paper introduces lower bounds and he...

In this paper we consider a more complicated real-world problem originating in the steel industry. The bins are inhomogeneous sheets with impurities. We assume that each impure area is rectangle. For each bin we are given a set of impurities, size, and location of each impurity into the bin. As a consequence now the bins are not identical anymore and the number of bins is finite. Moreover, we i...

In this paper we present approximation results for the class constrained bin packing problem that has applications to Video-on-Demand Systems. In this problem we are given bins of capacity B with C compartments, and n items of Q different classes, each item i ∈ {1, . . . , n} with class ci and size si. The problem is to pack the items into bins, where each bin contains at most C different class...

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. BestFit algorithm packs each item into the most full bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that th...

In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items, respectively) arrive over time, which must be packed into square bins of size 1×1. 90-rotation of an item is allowed. When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items. The objective is to minimize the t...