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Approximation algorithms for the selling with preference
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2020-06-11 , DOI: 10.1007/s10878-020-00602-3
Pan Li , Qiang Hua , Zhijun Hu , Hing-Fung Ting , Yong Zhang

We consider the market mechanism to sell two types of products, A and B, to a set of buyers \(I=\{1, 2, \ldots , n\}\). The amounts of products are \(m_A\) and \(m_B\) respectively. Each buyer i has his information including the budget, the preference and the utility function. On collecting the information from all buyers, the market maker determines the price of each product and allocates some amount of product to each buyer. The objective of the market maker is designing a mechanism to maximize the total utility of the buyers in satisfying the semi market equilibrium. In this paper, we show that this problem is NP-hard and give an iterative algorithm with the approximation ratio 1.5. Moreover, we introduce a PTAS for the problem, which is an (\(1+\epsilon \))-approximation algorithm with the running time \(O(2^{1/\epsilon }+n\log n)\) for any positive \(\epsilon \).

中文翻译:

偏好销售的近似算法

我们考虑了向一组买方\(I = \ {1,2,\ ldots,n \} \)销售两种类型的产品AB的市场机制。乘积的数量分别为\(m_A \)\(m_B \)。每个买家他的信息包括预算,偏好和效用函数。做市商从所有购买者那里收集信息后,便确定每种产品的价格,并将一定数量的产品分配给每个购买者。做市商的目标是设计一种机制,以使购买者在满足半市场均衡时的总效用最大化。在本文中,我们证明了该问题是NP难的,并给出了近似比率为1.5的迭代算法。此外,我们针对该问题引入了PTAS,它是运行时间为((O(2 ^ {1 / \ epsilon} + n \ log n)\)的(\(1+ \ epsilon \))近似算法对于任何正\(\ epsilon \)
更新日期:2020-06-11
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