In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D 3 dominates D 3 + λ(D 2 − D 1) for any λ ⩾ 0 if D 1 dominates D 2. Let U(D) be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that U(D ∞) and U(D ∈) are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Furthermore, the results are the generalized to integral flows.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Aug 7, 2017
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