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The scalable video coding (SVC) standard adopts the inter-layer residual prediction (ILRP) algorithm to encode the residual signal of the enhancement layer (EL). The ILRP reduces the number of bits required for encoding the residual signal but incurs excessive encoding time. In this paper, we propose a fast encoding algorithm for SVC-based video streaming. In this algorithm, the ILRP is selectively applied to the coding modes depending on their Lagrangian rate-distortion costs. Experimental results show that the proposed algorithm can reduce computational complexity with negligible video quality degradation and bitrate increments.