The maximum concurrent flow problem
Journal of the ACM (JACM)
Max-balancing weighted directed graphs and matrix scaling
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Lexicographically optimal balanced networks
IEEE/ACM Transactions on Networking (TON)
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Linear Programming Based Approach for Computing Optimal Fair Splittable Routing
ISCC '02 Proceedings of the Seventh International Symposium on Computers and Communications (ISCC'02)
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Routing, Flow, and Capacity Design in Communication and Computer Networks
Routing, Flow, and Capacity Design in Communication and Computer Networks
Communication nets; stochastic message flow and delay
Communication nets; stochastic message flow and delay
A unified framework for max-min and min-max fairness with applications
IEEE/ACM Transactions on Networking (TON)
Max-min fairness in multi-commodity flows
Computers and Operations Research
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In this paper, we introduce the lexicographically minimum load linear programming problem, and we provide a polynomial approach followed by the proof of correctness. This problem has applications in numerous areas where it is desirable to achieve an equitable distribution or sharing of resources. We consider the application of our technique to the problem of lexicographically minimum load in capacitated multicommodity networks and discuss a special nonlinear case, the so-called Kleinrock load function. We next define the lexicographically maximum load linear programming problem and deduce a similar approach. An application in the lexicographically maximum concurrent flow problem is depicted followed by a discussion on the minimum balance problem as a special case of the lexicographically maximum load problem.