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arXiv · 1601.07285

Fairness in Communication for Omniscience

Ni Ding·Chung Chan·Qiaoqiao Zhou·Rodney A. Kennedy·Parastoo Sadeghi
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Abstract

We consider the problem of how to fairly distribute the minimum sum-rate among the users in communication for omniscience (CO). We formulate a problem of minimizing a weighted quadratic function over a submodular base polyhedron which contains all achievable rate vectors, or transmission strategies, for CO that have the same sum-rate. By solving it, we can determine the rate vector that optimizes the Jain's fairness measure, a more commonly used fairness index than the Shapley value in communications engineering. We show that the optimizer is a lexicographically optimal (lex-optimal) base and can be determined by a decomposition algorithm (DA) that is based on submodular function minimization (SFM) algorithm and completes in strongly polynomial time. We prove that the lex-optimal minimum sum-rate strategy for CO can be determined by finding the lex-optimal base in each user subset in the fundamental partition and the complexity can be reduced accordingly.

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Ni Ding, Chung Chan, Qiaoqiao Zhou, Rodney A. Kennedy, Parastoo Sadeghi. 2016-01-27. Fairness in Communication for Omniscience. https://arxiv.org/abs/1601.07285

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