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Abstract Data warehouse and On-Line Analytical Processing (OLAP) are important components of Decision Support Systems (DSS). They are noticed in database systems more than every time. Now, there are many products and services for managing data warehousee and processing on-line analytical queries. On-line Analytical Processing (OLAP) systems have different requirements than On-Line Transactinal Processing (OLTP) systems. In this thesis, we first represent a comprehensive overview of data warehouse and OLAP. We describe back-end tools those extract data from different (and possibly herogeneus) databases, transform extracted data, and load transformed data in data warehouse. We also explain about front-end tools use for reporting, querying and analysing data. After that, we describe algorithms are represented for efficient query processing in data warehouses and specify advantages and drabacks of each algorithm. We represent a new approach for efficient cube computation by extending two best existing methodes: BUC and CCUBE. Results of implementation of this new method (Ex-CUBE), show this algorithm has the best efficiency between all previous algorithms. When we use Ex-Cube, processing time for monotonic queries in large amount of data, is very better than other algorithms. Moreover, Ex-Cube use a hypergraph structure called Ex-Graph for storing data. This graph causes we have a 2dimension view of cube. Thus Ex-cube’s space need, is less than other methods when we agreggate a subset of dimensions set. Keywords: Data warehouse, On-Line Analytical Processing (OLAP), Decision support systems, Multi-dimensional Data model, Data Cube,