Abstract

We describe a general paradigm for maintaining multidimensional keys in linked data structures. In particular, we show how to augment data structures de ned on one-dimensional keys so as to store, access and update eÆciently k-dimensional keys under the lexicographic order. While simple approaches produce an O(k) slowdown as a multiplicative factor in the running times of the original data structure, our method achieves a better O(k) additive term at the price of adding just few integers and pointers. As a result, we improve existing bounds and achieve new results in a simple way, without giving up the structural and topological properties of the underlying data structures. This is particularly important, as it allows us to exploit many properties of one-dimensional searching, and makes our approach amenable to practical implementations. 1 Introduction A vast repertoire of basic searching data structures, such as AVL-trees [1...

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