Approximation Algorithms for Secondary Spectrum Auctions

Abstract: 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 \Omega(n^{1-\epsilon}) 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.