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Previous studies have presented convincing arguments that a frequent pattern mining algorithm should not mine all frequent patterns but only the closed ones because the latter leads to not only more compact yet complete result set but also better efficiency. However, most of the previously developed closed pattern mining algorithms work under the candidate maintenance-and-test paradigm which is inherently costly in both runtime and space usage when the support threshold is low or the patterns become long. We present, BIDE, an efficient algorithm for mining frequent closed sequences without candidate maintenance. We adopt a novel sequence closure checking scheme called bidirectional extension, and prunes the search space more deeply compared to the previous algorithms by using the BackScan pruning method and the Scan-Skip optimization technique. A thorough performance study with both sparse and dense real-life data sets has demonstrated that BIDE significantly outperforms the previous algorithms: it consumes order(s) of magnitude less memory and can be more than an order of magnitude faster. It is also linearly scalable in terms of database size.