The emerging cube computed from two relations r_1, r_2 of categorical attributes gather the tuples for which the measure value strongly increases from r_1 to r_2. In this paper, we are interested in borders for emerging cubes which optimize both storage space and computation time. Such borders also provide classification and cube navigation tools. Firstly we study the condensed representation through the classical borders Lower / Upper, then we propose the borders Upper~* / Upper more reduced than the previous ones. We soundly state the connexion between the two representations by using cube transversals. Finally, we perform experiments about the size of the introduced representations. The results are convincing and reinforce our idea that the proposed borders are relevant candidates to be the smallest condensed representation of emerging cubes and thus can be really interesting for trend analysis in Olap databases.
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