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.

We describe our experience with CQA/CDB, a prototype rational linear constraint database. First, we show that the standard semantics of constraint databases lead to an anomaly when queried in the presence of missing attributes. In CQA/CDB, this anomaly is avoided by enriching the CDB relational schema, resulting in heterogenous databases. Then, we present spatial databases as a special case of heterogenous databases and extend constraint query algebras (CQAs) with two additional spatial operators, proving that the resulting language is safe for linear constraints.