Abstract: Free cube is a technique of reducing data cube size through mining the implication rules of dimension values in base table and removing the inherent redundancies in the structure of data cube While it is an interesting proposal, it leaves many issues unaddressed Firstly, a direct representation of a free cube is not as compact as possible and thus still wastes space Secondly, while a free cube can in principle be used for answering queries, no specific technique is given A new method is proposed to overcome these problems A storage based on graph structure called GSFC is given to exploit prefix redundancy when storing the free cube Meanwhile, GSFC combines the storage and indexing mechanism, and thus can efficiently solve the query of free cube Some algorithms are applied to directly construct GSFC from a base table and answer query using GSFC An experiment is presented to validate the efficiency of algorithms