Combinatorial problems related to origin-destination matrices

We consider the n-dimensional ternary Hamming space, T-n = {0, 1, 2}(n), and say that a subset L subset of or equal to T-n of three points form a line if they have exactly n - I components in common. A subset of T-n is called closed if, whenever it contains two points of a line, it contains also the third one. Finally, a generator is a subset, whose closure, the smallest closed set containing it, is T-n. In this paper, we investigate several combinatorial properties: of closed sets and generators, including the size of generators, and the complexity of generation. The present study was motivated by the problem of storing efficiently origin-destination matrices in transportation systems. (C) 2001 Elsevier Science B.V. All rights reserved.