A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

Xiang Yan, Wei Zhu

Abstract: The rapid growth of wireless and mobile Internet has led to wide applications of exchanging resources over network, in which how to fairly allocate resources has become a critical challenge. To motivate sharing, a BD Mechanism is proposed for resource allocation, which is based on a combinatorial structure called bottleneck decomposition. The mechanism has been shown with properties of fairness, economic efficiency [17], and truthfulness against two kinds of strategic behaviors [2, 3]. Unfortunately, the crux on how to compute a bottleneck decomposition of any graph is remain untouched. In this paper, we focus on the computation of bottleneck decomposition to fill the blanks and prove that the bottleneck decomposition of a network $$G=(V,E;w_v)$$ can be computed in $$O(n^6\log (nU))$$ , where $$n=|V|$$ and $$U=max_{v\in V}w_v$$ . Based on the bottleneck decomposition, a fair allocation in resource exchange system can be obtained in polynomial time. In addition, our work completes the computation of a market equilibrium and its relationship to two concepts of fairness in resource exchange.