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Contemporary data warehouses now represent some of the world's largest databases. As these systems grow in size and complexity, however, it becomes increasingly difficult for brute force query processing approaches to meet the performance demands of end users. In this paper, we describe the R3-cache, a natively multi-dimensional caching framework designed specifically to support sophisticated warehouse/OLAP environments. R3-cache is based upon an in-memory version of the R-tree that has been extended to support buffer pages rather than disk blocks. A key strength of the R 3-cache is that it is able to utilize multi-dimensional fragments of previous query results so as to significantly minimize the frequency and scale of disk accesses. Moreover, the new caching model directly accommodates the standard relational storage model and provides mechanisms for pro-active updates that exploit the existence of query "hot spots". The current prototype has been evaluated as a component of the Sidera DBMS, a "shared nothing" parallel OLAP server designed for multi-terabyte analytics. Experimental results demonstrate significant performance improvements relative to simpler alternatives.