To the best of our knowledge, this is the first algorithm unifying arbitrary rectilinear block packing and soft block packing. Furthermore, this algorithm handles arbitrary convex or concave rectilinear block packing in the most efficient way compared to other sequence pair-based approaches. At the same time, the algorithm can handle rectangle soft block effectively. The concept of non-redundan...

Background: Saffron, the dried stigmas of crocus sativus, is the world's most expensive spice which has been used as food additive and flavoring agent. The aim of the present study has been to investigate the combination effects of gamma irradiation and silver nano particles packing on the chemical properties of saffron during storage time. A combination of hurdles can ensure stability a...

The strip packing problem is to pack a set of rectangles into a strip of fixed width and minimum length. We present asymptotic polynomial time approximation schemes for this problem without and with 90o rotations. The additive constant in the approximation ratios of both algorithms is 1, improving on the additive term in the approximation ratios of the algorithm by Kenyon and Rémila (for the pr...

Haxell’s condition [Hax95] is a natural hypergraph analog of Hall’s condition, which is a wellknown necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell’s condition holds it forces the existence of a perfect matching in the bipartite hypergraph. Unlike in graphs, however, there is no known polynomial time algorithm to find the hypergraph per...

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...

We provide the directed counterpart of a slight extension of Katoh and Tanigawa’s result [8] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds’ result [1] on packing of spanning arborescences and implies – using a general orientation result of Frank [4] – the a...

We prove that every set of squares with total area 1 can be packed into a rectangle of area at most 2867/2048 = 1.399. . . . This improves on the previous best bound of 1.53. Also, our proof yields a linear time algorithm for finding such a packing.