Combinatorial problems related to origin–destination matrices

• Published in: Discrete Applied Mathematics Vol. 115; no. 1; pp. 15 - 36
• Main Authors: Boros, Endre, Hammer, Peter L., Ricca, Federica, Simeone, Bruno
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 15.11.2001; Amsterdam Elsevier; New York, NY
• Subjects: Classical combinatorial problems; Combinatorics; Combinatorics. Ordered structures; Exact sciences and technology; Generator; Hamming space; Mathematics; Origin–destination matrix; Sciences and techniques of general use; Hamming space; Origin–destination matrix; Generator; Origin destination matrix; Hamming distance; Hamming space genrator; Combinatorial problem; hamming space; Symmetric difference
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/S0166-218X(01)00212-8

We consider the n-dimensional ternary Hamming space, T n={0,1,2} n , and say that a subset L⊆ T n of three points form a line if they have exactly n−1 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.