We consider the n-dimensional ternary Hamming space, T^n ={0; 1; 2}^n,and say that a subset L ⊆ Tn 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 effciently origin–destination matrices in transportation systems.
Combinatorial Problems Related to Origin-Destination Matrices / E., Boros; P. L., Hammer; Ricca, Federica; B., Simeone. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 115:(2001), pp. 15-36. [10.1016/S0166-218X(01)00212-8]
Combinatorial Problems Related to Origin-Destination Matrices
RICCA, Federica;
2001
Abstract
We consider the n-dimensional ternary Hamming space, T^n ={0; 1; 2}^n,and say that a subset L ⊆ Tn 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 effciently origin–destination matrices in transportation systems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
