The distance geometry problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, inc...
The problem addressed in this paper is that of orthogonally packing a given set of box-shaped items into the minimum number of three-dimensional rectangular and equal bins. The problem is NP-hard in the strong sense and extremely difficult to be solved in the practice. We introduce a new heuristic for the problem based upon the way the items fit a given bin which is dictated by two lists: corner points and item...
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