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Multidimensional data points can be mapped to one-dimensional space to exploit single dimensional indexing structures such as the B+-tree. In this article we present a Generalized structure for data Mapping and query Processing (GiMP), which supports extensible mapping methods and query processing. GiMP can be easily customized to behave like many competent indexing mechanisms for multi-dimensional indexing, such as the UB-Tree, the Pyramid technique, the iMinMax, and the iDistance. Besides being an extendible indexing structure, GiMP also serves as a framework to study the characteristics of the mapping and hence the efficiency of the indexing scheme. Specifically, we introduce a metric called mapping redundancy to characterize the efficiency of a mapping method in terms of disk page accesses and analyze its behavior for point, range and kNN queries. We also address the fundamental problem of whether an efficient mapping exists and how to define such a mapping for a given data set.