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Spectrum auction is an effective approach to improve the spectrum utilization, by leasing an idle spectrum from primary users to secondary users. Recently, a few differentially private spectrum auction mechanisms have been proposed, but, as far as we know, none of them addressed the differential privacy in the setting of double spectrum auctions. In this paper, we combine the concept of differential privacy with double spectrum auction design and present a differentially private double spectrum auction mechanism with approximate social welfare maximization (DDSM). Specifically, we design the mechanism by employing the exponential mechanism to select clearing prices for the double spectrum auction with probabilities exponentially proportional to the related social welfare values and then improve the mechanism in several aspects, such as the designs of the auction algorithm, the utility function, and the buyer grouping algorithm. Through theoretical analysis, we prove that DDSM achieves differential privacy, approximate truthfulness, and approximate social welfare maximization. Extensive experimental evaluations show that DDSM achieves a good performance in terms of social welfare.
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