We investigate bandwidth allocation and scheduling in non-cooperative wireless networks as a mixed integer programming problem. Fast Vickrey-Clarke-Groves (VCG) auctionbased bandwidth allocation (FABA), incorporating relaxationbased greedy algorithm (RGA) and split-flow-based algorithm (SFA), is proposed by modifying the traditional VCG auction to make it computationally feasible. With incentives provided by FABA, the dominant strategy of any selfish node in the network is to be cooperative so that the system cost is minimized. We implement FABA via a batching-based mechanism which allocates bandwidth for all call routing requests arriving in a certain batching period simultaneously. Our simulation evaluates the performance in terms of system cost, payment-cost ratio, and setup time.