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In this paper, we present a novel algorithm for mining complete frequent itemsets. This algorithm is referred to as the TM (transaction mapping) algorithm from hereon. In this algorithm, transaction ids of each itemset are mapped and compressed to continuous transaction intervals in a different space and the counting of itemsets is performed by intersecting these interval lists in a depth-first order along the lexicographic tree. When the compression coefficient becomes smaller than the average number of comparisons for intervals intersection at a certain level, the algorithm switches to transaction id intersection. We have evaluated the algorithm against two popular frequent itemset mining algorithms, FP-growth and dEclat, using a variety of data sets with short and long frequent patterns. Experimental data show that the TM algorithm outperforms these two algorithms.