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Cognitive radio (CR) is a promising technology to solve the spectrum scarcity problem by enabling secondary users (SU) to utilize the spectrum holes of primary users (PU) caused by static spectrum allocation. However, SUs need to avoid the interference to PUs, imposing new challenges in routing protocol designs and throughput improvement in CR networks (CRN). In this paper we propose a cross-layer channel assignment and routing (CCAR) algorithm. Specifically, our CCAR algorithm aims at throughput maximization while addressing the interference avoidance issue in CRNs. Solving for the optimal solution towards throughput maximization is a NP problem. In contrast, we simplify this optimization problem by taking advantage of the correlation of data flow and routing information across the network nodes. Then, further making use of the adjacent hop interference (AHI) Information, we develop a heuristic approach to obtain a suboptimal solution. Theoretical analysis and simulation results show that our proposed CCAR algorithm can achieve polynomial complexity at the cost of only 20% throughput loss as compared to the optimal solution.