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A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

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Frontiers in Algorithmics (FAW 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11458))

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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.

Supported by the National Nature Science Foundation of China (No. 11301475, 61632017, 61761146005).

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Correspondence to Xiang Yan .

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Yan, X., Zhu, W. (2019). A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_1

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  • DOI: https://doi.org/10.1007/978-3-030-18126-0_1

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