We design algorithms with linear time complexity with respect to the dimension for three commonly studied correlation structures, including exchangeable, decaying-product and K-dependent correlation structures, and extend the algorithms to generate binary data of general non-negative correlation matrices with quadratic time complexity. Jiang, W., Song, S., Hou, L. and Zhao, H. "CorBin: An efficient R package to generate high-dimensional binary data with correlation structures." Submitted to Journal of Statistical Software.