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Software defined radio (SDR) capitalizes advances in signal processing and radio technology and is capable of reconfiguring RF and switching to desired frequency bands. It is a frequency-agile data communication device that is vastly more powerful than recently proposed multi-channel multi-radio (MC-MR) technology. In this paper, we investigate the important problem of multi-hop networking with SDR nodes. For such network, each node has a pool of frequency bands (not necessarily of equal size) that can be used for communication. The uneven size of bands in the radio spectrum prompts the need of further division into sub-bands for optimal spectrum sharing. We characterize behaviors and constraints for such multi-hop SDR network from multiple layers, including modeling of spectrum sharing and sub-band division, scheduling and interference constraints, and flow routing. We give a formal mathematical formulation with the objective of minimizing the required network-wide radio spectrum resource for a set of user sessions. Since such problem formulation falls into mixed integer non-linear programming (MINLP), which is NP-hard in general, we develop a lower bound for the objective by relaxing the integer variables and linearization. Subsequently, we develop a near-optimal algorithm to this MINLP problem. This algorithm is based on a novel sequential fixing procedure, where the integer variables are determined iteratively via a sequence of linear programming. Simulation results show that solutions obtained by this algorithm are very close to lower bounds obtained via relaxation, thus suggesting that the solution produced by the algorithm is near-optimal.