A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

• Published in: Frontiers in Algorithmics Vol. 11458; pp. 1 - 13
• Main Authors: Yan, Xiang, Zhu, Wei
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Bottleneck decomposition; Fair allocation; Polynomial algorithm; Resource exchange
• ISBN: 3030181251; 9783030181253
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-18126-0_1

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;wv) $$G=(V,E;w_v)$$ can be computed in O(n6log(nU)) $$O(n^6\log (nU))$$ , where n=|V| $$n=|V|$$ and U=maxv∈Vwv $$U=max_{v\in V}w_v$$ . 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.