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Previous studies on supporting free-form keyword queries over RDBMSs provide users with linked structures (e.g., a set of joined tuples) that are relevant to a given keyword query. Most of them focus on ranking individual tuples from one table or joins of multiple tables containing a set of keywords. In this paper, we study the problem of keyword search in a data cube with text-rich dimension(s) (so-called text cube). The text cube is built on a multidimensional text database, where each row is associated with some text data (a document) and other structural dimensions (attributes). A cell in the text cube aggregates a set of documents with matching attribute values in a subset of dimensions. We define a keyword-based query language and an IR-style relevance model for scoring/ranking cells in the text cube. Given a keyword query, our goal is to find the top-k most relevant cells. We propose four approaches: inverted-index one-scan, document sorted-scan, bottom-up dynamic programming, and search-space ordering. The search-space ordering algorithm explores only a small portion of the text cube for finding the top-k answers, and enables early termination. Extensive experimental studies are conducted to verify the effectiveness and efficiency of the proposed approaches.