Association rule data mining is an important technique for finding important relationships in large datasets. Several frequent itemsets mining techniques have been proposed using a prefix-tree structure, FP-tree, a compressed data structure for database representation. The DIFFset data structure has also been shown to significantly reduce the run time and memory utilization of some data mining algorithms. Experimental results have demonstrated the efficiency of the two data structures in frequent itemsets mining. This work proposes FDM, a new algorithm based on FP-tree and DIFFset data structures for efficiently discovering frequent patterns in data. FDM can adapt its characteristics to efficiently mine long and short patterns from both dense and sparse datasets. Several optimization techniques are also outlined to increase the efficiency of FDM. An evaluation of FDM against three frequent itemset data mining algorithms, dEclat, FP-growth, and FDM* (FDM without optimization), was performed using datasets having both long and short frequent patterns. The experimental results show significant improvement in performance compared to the FP-growth, dEclat, and FDM* algorithms.