With the exponential growth of time series data, Piecewise Linear Approximation under the maximum error bound (PLA \(_{\infty }\) ) has regained significant attention due to its outstanding compression capabilities. Traditional PLA \(_{\infty }\) algorithms typically offer a significantly higher compression ratio than lossless techniques, but their advantage diminishes as error bounds become stricter. To overcome this limitation, this paper introduces two innovative merge-based PLA \(_{\infty }\) algorithms: HuffSwingSeg and HuffOptSeg. These algorithms initially apply distinct segmentation methods, Swing for HuffSwingSeg and OptimalPLR for HuffOptSeg. They then utilize a “twice-merging” approach to merge segments independently based on slopes and starting point values. This process further decreases the number of segment items by using map structures and Huffman coding. Experimental results demonstrate that these methods outperform advanced Mix-Piece algorithm 1.1–1.3 times on average in the compression ratio under strict error bounds with only a moderate increase in time costs.