We prove that Best Fit bin packing has linear waste on the discrete distributionU{j, k} (where items are drawn uniformly from the set {1/k, 2/k, · · · , j/k}) for sufficiently large k when j = αk and 0.66 ≤ α < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 ≤ a < 2/3. This implies that the expected asymptotic performance ratio of ...

Given a tournament T and a positive integer k, the C3-Packing-T problem asks if there exists a least k (vertex-)disjoint directed 3-cycles in T . This is the dual problem in tournaments of the classical minimal feedback vertex set problem. Surprisingly C3-Packing-T did not receive a lot of attention in the literature. We show that it does not admit a PTAS unless P=NP, even if we restrict the co...

The packing of helices spanning lipid bilayers is crucial for the stability and function of alpha-helical membrane proteins. Using a modified Voronoi procedure, we calculated packing densities for helix-helix contacts in membrane spanning domains. Our results show that the transmembrane helices of protein channels and transporters are significantly more loosely packed compared with helices in g...

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...

Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems, no single method has emerged that matches the effectiveness and simplicity afforded by the covering case. We offer a simple iterative packing technique that ...

This article aims to tackle a practical three-dimensional packing problem, where a number of cartons of diverse sizes are to be packed into a bin with fixed length and width but open height. Each carton is allowed to be packed in any one of the six orientations, and the carton edges are parallel to the bin edges. The allowance of variable carton orientations exponentially increases the solution...

Packing of about two meters of the human genome DNA into chromatin occupying a several micron-sized cell nucleus requires a high degree of compaction in a manner that allows the information encoded on DNA to remain easily accessible. This packing is mediated by repeated coiling of DNA double helix around histones to form nucleosome arrays that are further folded into higher-order structures. Re...

Product quality for plastic injection molding process is highly related with the settings for its process parameters. Additionally, the product quality is not simply based on a single quality index, but multiple interrelated quality indices. To find the settings for the process parameters such that the multiple quality indices can be simultaneously optimized is becoming a research issue and ...

The 1TW7 crystal structure of HIV-1 protease shows the flaps placed wider and more open than what is seen in other examples of the semi-open, apo form. It has been proposed that this might be experimental evidence of allosteric control, because crystal packing creates contacts to the "elbow region" of the protease, which may cause deformation of the flaps. Recent dynamics simulations have shown...