In this work, we study spectrum auction problem where each request fromsecondary users has spatial, temporal, and spectral features. With the requestsof secondary users and the reserve price of the primary user, our goal is todesign truthful mechanisms that will either maximize the social efficiency ormaximize the revenue of the primary user. As the optimal conflict-free spectrumallocation problem is NP-hard, in this work, we design near optimal spectrumallocation mechanisms separately based on the following techniques:derandomized allocation from integer programming formulation, its linearprogramming (LP) relaxation, and the dual of the LP. We theoretically provethat 1) our near optimal allocation methods are bid monotone, which implystruthful auction mechanisms; and 2) our near optimal allocation methods canachieve a social efficiency or a revenue that is at least $1-\frac{1}{e}$ timesof the optimal respectively. At last, we conduct extensive simulations to studythe performances (social efficiency, revenue) of the proposed methods, and thesimulation results corroborate our theoretical analysis.
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