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- W24692802 abstract "In this thesis, we address the problem of allocating fixed resources among users in some fair fashion. Although the issue of fairness has been studied in many areas by many people, there are diverse definitions for fairness such as max-min fairness, proportional fairness, minimum variance, and so on. To deal with this complexity, a novel framework called majorization was recently suggested, which simultaneously satisfies a large class of fairness criteria. This is what this thesis studies. We develop practical algorithms which simultaneously achieve multiple fairness objectives. The fairness criteria we consider are the class of utility functions which span a very large area of fairness measurement functions. Specifically, what we want to design is a simple distributed algorithm which approximately maximizes all kinds of canonical utility functions simultaneously. For the realization of distributed algorithms, we use primal-dual linear programming approach and concept of agents. We present that the proper interactions between flow agents and edge agents induce a solution which almost maximizes all the canonical utility functions simultaneously. We present distributed algorithms to solve the abovementioned problem through two steps. First, we show how to adapt primal and dual linear programmings to the simultaneous optimization problem. Then, we extend the result to a distributed algorithm which uses only local communication between flow agents and edge agents, i.e., the communication takes place only between a flow agent and edge agents on the path of the flow. We prove that the first algorithm requires at most O(m log m) iterations of a primal-dual update and the latter requires at most O(nR log(m + n + R)) iterations where m is the number of edges, n is the number of flows, and R is the ratio of maximum edge capacity to the minimum edge capacity. The former algorithm guarantees a O (log n + log R)-approximate solution, and the latter algorithm guarantees a O(log m + log n + log R)-approximate solution." @default.
- W24692802 created "2016-06-24" @default.
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- W24692802 date "2005-01-01" @default.
- W24692802 modified "2023-09-28" @default.
- W24692802 title "Distributed resource allocation in networks for multiple concave objectives" @default.
- W24692802 hasPublicationYear "2005" @default.
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