New Discoveries of Domination Between Traffic Matrices

作     者：Peng-fei LIU Wen-guo YANG Tian-de GUO 

作者机构：School of Mathematics SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge ManagementChinese Academy of SciencesBeijing 100049China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2017年第33卷第3期

页      面：561-566页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China under Grant No.(1157101511331012) the Open Project of Key Laboratory of Big Data Mining and Knowledge Management Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No.(KGCX2-RW-329) 

主　　题：robust network design multi-commodity flows domination 

摘      要：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 D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. 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. Fhrthermore, the results are the generalized to integral flows.