In this paper, the effects of two different Particle Size Distributions (PSD) on packingbehavior of ideal rigid spherical nanoparticles using a novel packing model based on parallelalgorithms have been reported. A mersenne twister algorithm was used to generate pseudorandomnumbers for the particles initial coordinates. Also, for this purpose a nanosized tetragonal confinedcontainer with a squar...

We consider the bin-packing problem with the constraint that the elements are in the plane, and only elements within an oriented unit square can be placed within a single bin. The elements are of given weights, and the bins have unit capacities. The problem is to minimize the number of bins used. Since the problem is obviously NP-hard, no algorithm is likely to solve the problem optimally in be...

Recently Bansal and Sviridenko [4] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Rectangle Bin Packing without rotations allowed, unless P = NP. We show that similar approximation hardness results hold for several rectangle packing problems even if rotations by ninety degrees around the axes are allowed. Moreover, for some of these problems we provide explicit lower bound...

Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given O(1/ǫ) advice bits for each input item allows approximating the dual bin packing problem online to within a factor of 1 + ǫ. Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this q...

The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π , an optimal solution OPT for Π in I and an instance I ′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I ′, either optimally or by guaranteeing an approximation ratio better than ...

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...

The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the "HARMONIC" algorithms Hk introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562-572 ]. The algorithms in this paper guarantee the worst case performance of Hk, whereas they only use O(log log k) instead ofk active bins. For k >_6, the algorithms in this paper outpe...

We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The speci"c application is the allocation of excess of a population of various types of cards (e.g., left over from a previous selling season) to "xed-sized &&variety packs'' whic...

In this paper, we consider the maximum weight ({K1,K2},k,l)-packing problem in a graph. This generalizes number of well-known problems, for example: induced matching, k-separated connected independent set, dissociating k-packing. We show that class cographs, ({K1,K2},k,l)- packing can be computed O(n + m) time. Let Γ graphs and Γ* all simple (with respect to modular decomposition) subgraphs fro...

Bansal and Sviridenko [4] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P = NP. We show that similar approximation hardness results hold for several 2and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asym...