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The condensed cube has been proposed to reduce the huge size of data cubes in OLAP system. The intuition of condensed cube is to compress semantically redundant tuples into their representative base single tuples (BSTs). However, previous studies showed that a minimal condensed cube is expensive to compute, and thus mainly concentrated on alternative computation methods for non-minimal condensed cube, which does not guarantee to find and compress all BSTs. In this paper, we focus on the minimal condensed cube and address several practical issues, including physical organization, fast computation, and incremental update. Experiments on both synthetic and real-world datasets show that our proposed algorithms outperform previous methods by a large margin.