Introduction to algorithms
A decomposition problem of a natural number for a rectangular cutting-covering model
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
A topological order for a rectangular covering problem
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
A topological order for a rectangular three dimensional bin packing problem
ICCOMP'08 Proceedings of the 12th WSEAS international conference on Computers
An algorithm for the guillotine restrictions verification in a rectangular covering model
WSEAS Transactions on Computers
WSEAS Transactions on Computers
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We consider the rectangular three dimensional bin packing problem with knapsack, where the bin is packed with a set of rectangular boxes, without gaps or overlapping. Starting from a solution of the three dimensional bin packing model, our objective is to determine an order of the loading the boxes in the bin so that a box will be packed in the bin only if there are no empty spaces down to this box and the origin of the box is in a fixed position, determinated by the boxes situated in the West and North neighbourhood. By extension of the previous work regarding the two dimensional covering problem [12] and the three dimensional bin packing problem [15], we define three kind of adjacency relations between two boxes from a packing model, similarly with [13, 14]. Combining these relations we define an acyclic graph representation of the bin packing model. A plan for lauding of the boxes in the bin is obtained using a topological sorting algorithm of the vertices of this acyclic graph.