  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.
