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Interference alignment (IA) is a joint-transmission technique for the interference channel that achieves the maximum degrees-of-freedom and provides linear scaling of the capacity with the number of users for high signal-to-noise ratios (SNRs). Most prior work on IA is based on the impractical assumption that perfect and global channel-state information (CSI) is available at all transmitters. However, to implement IA, each receiver has to feed back CSI to all interferers, resulting in overwhelming feedback overhead. In particular, the sum feedback rate of each receiver scales quadratically with the number of users even if the feedback CSI is quantized. To substantially suppress feedback overhead, this paper focuses on designing efficient arrangements of feedback links, called feedback topologies, under the IA constraint. For the multiple-input multiple-output (MIMO) K-user interference channel, we propose the feedback topology that supports sequential CSI exchange (feedback and feedforward) between transmitters and receivers so as to achieve IA progressively. This feedback topology is shown to reduce the network feedback overhead from a quadratic function of K to a linear one. To reduce the delay in the sequential CSI exchange, an alternative feedback topology is designed for supporting two-hop feedback via a control station, which also achieves the linear feedback scaling with K. Next, given the proposed feedback topologies, the feedback-bit allocation algorithm is designed for allocating feedback bits by each receiver to different feedback links so as to regulate the residual interference caused by finite-rate feedback. Simulation results demonstrate that the proposed bit allocation leads to significant throughput gains especially in strong interference environments.