二次频谱拍卖的近似算法
Approximation Algorithms for Secondary Spectrum Auctions
摘要：
我们研究了二级频谱市场的组合拍卖。在这个市场中，短期许可证应给予无线节点在其本地邻域中进行通信。与一级市场相反，只要相应的设备被很好地分开，使得干扰足够低，就可以将信道分配给多个投标人。干扰冲突描述的冲突图，其中的节点表示投标人和边缘表示冲突，使得信道的可行分配对应于冲突图中的独立集。在本文中，我们提出了一个新的LP制定的组合拍卖与冲突图使用非标准的图参数，所谓的归纳独立数。考虑到这个参数，使我们能够绕过众所周知的Ω（n^{1-ε}）的下限的独立集在一般图的n个节点（投标人）的逼近。我们实现了显着更好的近似结果表明，无线网络的干扰约束产生冲突图有界归纳独立数。我们的框架涵盖了各种已建立的无线通信模型，例如，协议或物理模型。对于协议模型，我们实现了O（\sqrt{k}）-近似，其中k是可用信道的数量。对于更真实的物理模型，我们实现了一个O（\sqrt{k} \log^2 n）的近似基于边加权冲突图。结合我们的方法与LP为基础的框架拉维和斯瓦米，我们获得激励兼容的机制，为一般投标人的任意估值捆绑指定的渠道方面的需求预言。
英文摘要：
We study combinatorial auctions for the secondary spectrum market. In this market, short-term licenses shall be given to wireless nodes for communication in their local neighborhood. In contrast to the primary market, channels can be assigned to multiple bidders, provided that the corresponding devices are well separated such that the interference is sufficiently low. Interference conflicts are described in terms of a conflict graph in which the nodes represent the bidders and the edges represent conflicts such that the feasible allocations for a channel correspond to the independent sets in the conflict graph. In this paper, we suggest a novel LP formulation for combinatorial auctions with conflict graph using a non-standard graph parameter, the so-called inductive independence number. Taking into account this parameter enables us to bypass the well-known lower bound of Ω(n^{1-ε}) on the approximability of independent set in general graphs with n nodes (bidders). We achieve significantly better approximation results by showing that interference constraints for wireless networks yield conflict graphs with bounded inductive independence number. Our framework covers various established models of wireless communication, e.g., the protocol or the physical model. For the protocol model, we achieve an O(\sqrt{k})-approximation, where k is the number of available channels. For the more realistic physical model, we achieve an O(\sqrt{k} \log^2 n) approximation based on edge-weighted conflict graphs. Combining our approach with the the LP-based framework of Lavi and Swamy, we obtain incentive compatible mechanisms for general bidders with arbitrary valuations on bundles of channels specified in terms of demand oracles.
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