A lower bound theorem for indexing schemes and its application to multidimensional range queries

Summarization: Indexing schemes were proposed by Hellerstein, Koutsoupias and Fapadlmitriou [7] to model data indexing on external memory, Using indexing schemes, the complexity of indexing is qunntified by two parameters: storage redundancy and access overhead, There is a tradeoff between these two parameters, in the sense that for some problems it is not poseiblc for both of these to be low. In this paper we derive a lower-bounds theorem for arbitrary indexing schemes. We apply our theorem to the particular problem of d-dimensional range queries. We first resolve the open problem of [7] for a tight lower bound for 2-dimensional range queries and extend our lower bound to &dimensional range queries. We then show, how, the construction in our lower-bounds proof may be exploited to derive indexing schemes for d-dimensional range queries, whose asymptotic complexity matches our lower bounds.Παρουσιάστηκε στο: Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database System

Abstract A Lower Bound Theorem for Indexing Schemes and its Application to Multidimensional Range Queries *

and Fapadlmitriou [7] to model data indexing on external memory, Using indexing schemes, the complexity of index-ing is qunntified by two parameters: storage redundancy and access overhead, There is a tradeoff between these two parameters, in the sense that for some problems it is not poseiblc for both of these to be low. In this paper we derive a lower-bounds theorem for ar-bitrary indexing schemes. We apply our theorem to the particular problem of d-dimensional range queries. We first resolve the open problem of [7] for a tight lower bound for 2-dimensional range queries and extend our lower bound to &dimensional range queries. We then show, how, the con-struction in our lower-bounds proof may be exploited to de-rive indexing schemes for d-dimensional range queries, whose asymptotic complexity matches our lower bounds.