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• Customizing general frequent pattern mining algorithms to efficient Top-Rank-K ones. • Employing Dynamic Minimum Support Threshold Raising strategy to ensure efficiency. • Outperforming BTK algorithm with a 90% runtime improvement. • Experiments on real and synthetic datasets including Connect and Retail. Mining frequent patterns (FP) is an essential task in data mining. The parameter required for this task is typically the minimum support threshold. Tuning this parameter to a suitable value is a difficult task, especially for inexperienced users. Thus, the Top-Rank-K frequent patterns mining problem was introduced. It requires the user to input an easily-evaluated parameter, K , in order to obtain the set of all frequent patterns from the most frequent to the K th rank of frequency. In this paper, we customize three general Frequent Pattern Mining (FPM) algorithms, namely FIN, PrePost, and PrePost+, to develop specialized Top-Rank-K FP mining algorithms: TK_FIN, TK_PrePost, and TK_PrePost+. The Dynamic Minimum Support Raising strategy is applied on these algorithms to ensure efficiency. Experimentally, we evaluate the performance of these algorithms against an original, efficient, Top-Rank-K algorithm, BTK. The three presented algorithms perform 90% better than BTK in most of the experiments, with respect to runtime. Between the three Top-Rank-K FPM algorithms we present, TK_FIN achieves the best performance from both runtime and memory consumption perspectives. [ABSTRACT FROM AUTHOR]