In this paper we use the novel concept of minimal cube transversals on the cube lattice of a categorical database relation for mining the borders of the difference of two datacubes. The problem of finding cube transversals is a sub-problem of hypergraph transversal discovery since there exists an order-embedding from the cube lattice to the power set lattice of binary attributes. Based on this result, we propose a levelwise algorithm and an optimization which uses the frequency of the disjunction for mining minimal cube transversals. Using cube transversals, we introduce a new OLAP functionality: discovering the difference of two uni-compatible datacubes or the most frequent elements in the difference. Finally we propose a merging algorithm for mining the boundary sets of the difference without computing the two related datacubes. Provided with such a difference of two datacubes capturing similar informations but computed at different dates, a user can focus on what is new or more generally on how evolve the previously observed trends.
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