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This paper critically analyzes reduct construction methodsat two levels. At a high level, one can abstract commonalities from theexisting algorithms, and classify them into three basic groups based onthe underlying control structures. At a low level, by adopting differentheuristics or fitness functions for attribute selection, one is able to derivemost of the existing algorithms. The analysis brings new insights into theproblem of reduct construction, and provides guidelines for the design ofnew algorithms.