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Closed cube computation is a popular method to solve the huge output problem of data cubing and has attracted great interests among researchers. A lot of efficient algorithms such as QC-DFS, C-Cubing and CC ALG have been proposed. However, due to significant changes in computer hardware architecture in recent years, these algorithms need to be revisited to achieve good performance. In this paper, we present a parallel algorithm for closed cube computation on multi-core CPUs to fully utilize the processor resources. In our algorithm, a cost-based load balance strategy is designed to deal with data skews and partitions based on each individual dimension are simultaneously computed to generate closed cells. An extensive performance study is conducted and the results show that good speedups can be gained for the parallel algorithm.