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As the complexity of digital filters is dominated by the number of multiplications, many works have focused on minimizing the complexity of multiplier blocks that compute the constant coefficient multiplications required in filters. Although the complexity of multiplier blocks is significantly reduced by using efficient techniques such as decomposing multiplications into simple operations and sharing common subexpressions, previous works have not considered the delay of multiplier blocks which is a critical factor in the design of complex filters. In this paper, we present new algorithms to minimize the complexity of multiplier blocks under the given delay constraints. By analyzing multiplier blocks in view of delay, three delay reduction methods are proposed and combined into previous algorithms. Since the proposed algorithms can generate multiplier blocks that meet the specified delay, a trade-off between delay and hardware complexity is enabled by changing the delay constraints. Experimental results show that the proposed algorithms can reduce the delay of multiplier blocks at the cost of a little increase of complexity.