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We study the performance issue of the "iterative" record linkage (RL) problem, where match and merge operations may occur together in iterations until convergence emerges. We first propose the Iterative Locality-Sensitive Hashing (ILSH) that dynamically merges LSH-based has tables for quick and accurate blocking. Then, by exploiting inherent characteristics within/across data sets, we develop a suite of I-LSH-based RL algorithms, named as HARRA. The superiority of HARRA in speed over competing RL solutions is thoroughly validated using various real data sets. While maintaining equivalent or comparable accuracy levels, for instance, HARRA runs: (1) 4.5 and 10.5 times faster than StringMap and R-Swoosh in iteratively linking 4,000 x 4,000 short records (i.e., one of the small test cases), and (2) 5.6 and 3.4 times faster than basic LSH and Multi-Probe LSH algorithms in iteratively linking 400,000 x 400,000 long records (i.e., the largest test case).