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Frequent itemset mining has been studied extensively in literature. Most previous studies require the specification of a min_support threshold and aim at mining a complete set of frequent itemsets satisfying min_support. However, in practice, it is difficult for users to provide an appropriate min_support threshold. In addition, a complete set of frequent itemsets is much less compact than a set of frequent closed itemsets. In this paper, we propose an alternative mining task: mining top-k frequent closed itemsets of length no less than min_l, where k is the desired number of frequent closed itemsets to be mined, and min_l is the minimal length of each itemset. An efficient algorithm, called TFP, is developed for mining such itemsets without mins_support. Starting at min_support = 0 and by making use of the length constraint and the properties of top-k frequent closed itemsets, min_support can be raised effectively and FP-Tree can be pruned dynamically both during and after the construction of the tree using our two proposed methods: the closed node count and descendant_sum. Moreover, mining is further speeded up by employing a top-down and bottom-up combined FP-Tree traversing strategy, a set of search space pruning methods, a fast 2-level hash-indexed result tree, and a novel closed itemset verification scheme. Our extensive performance study shows that TFP has high performance and linear scalability in terms of the database size.