In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.

This report describes a recursive process for generating data sets of rigid rectangles that can be placed into rectangular regions with zero waste. The generation procedure can be modified to guarantee that the aspect and area ratios of the rectangles in the generated data sets satisfy user-specified parameters. This recursive process can thus be employed to create a variety of data sets that c...

Aboveground production in terrestrial plant communities is commonly expressed in amount of carbon, or biomass, per unit surface. Alternatively, expressing production per unit volume allows the comparison of communities by their fundamental capacities in packing carbon. In this work we reanalyzed published data from more than 900 plant communities across nine ecosystems to show that standing dry...

We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. To achieve this, we introduce a new technique for classifying the items to be packed. We show that our algorithm is optimal among bounded space algorithms for any dimension d > 1. Its asymptotic performance ratio is (Π∞) , where Π∞ ≈ 1.691 is the asymptotic ...

This study was performed among workers of an Iranian pharmaceutical industry with the aiming to determine WRMDs prevalence and exposure assessment of WRMDs risks. In this cross-sectional study, 84 female and male workers randomly selected from five packing operations. Modified Nordic Musculoskeletal Questionnaire (NMQ) was applied to study the prevalence of WRMDs and Rapid Upper Limb Assessment...

The packing layout for loading boxes of identical format on a pallet can be determined algorithmically. This is important when performing automated packing by a robot. The well-known four-block heuristics and G4heuristics produce very efficient loading patters in most practical cases. In addition to the number of boxes on the pallet, one has to maximize the stability of the loading. This paper ...

A parallel version of the modified billiard algorithm has been implemented to solve larger instances of the static packing problem i.e., given a number of discs, compute the maximum radius such that the discs fit within the unit square without overlapping [1]. An existing serial algorithm available at [2] was taken as a basis and modified towards the main objective of this project, high perform...