We continue the study of two recently introduced bin packing type problems, called with clustering, and online delays. A input consists items sizes not larger than 1, goal is to partition or pack them into bins, where total size every valid cannotexceed 1. In also have colors associated them. globally optimal solution can combine different while a clustered only monochromatic bins. The compare ...

When analyzing neuron spike trains, it is always the problem of how to set the time bin. Bin width affects much to analyzed results of such as periodicity of the spike trains. Many approaches have been proposed to determine the bin setting. However, these bins are fixed through the analysis. In this paper, we propose a randomizing method of bin width and location instead of conventional fixed b...

In the bin packing problem, we get a sequence of packets of size r 1 ; r 2 ; r 3 ; : : :, each r i 1, and we must place the packets into bins of size 1 using as few bins as possible. The size of a bin is the accumulated size of all packets in the bin, and the free capacity of a bin is 1 minus its size.

We consider two related optimization problems: bin-packing with fragile objects and frequency allocation in cellular networks. The former is a generalization of the classical bin packing problem and is motivated by the latter. The problem is as follows: Each object has two attributes, weight and fragility. The goal is to pack objects into bins such that, for every bin, the sum of weights of obj...

In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional sp...

We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (aminimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the mo...