Multidimensional declustering schemes using Golden Ratio and Kronecker Sequences

We propose a new declustering scheme for allocating uniform multidimensional data among parallel disks. The scheme, aimed at reducing disk access time for range queries, is based on Golden Ratio Sequences for two dimensions and Kronecker Sequences for higher dimensions. Using exhaustive simulation, we show that, in two dimensions, the worst-case (additive) deviation of the scheme from the optimal response time for any range query is one when the number of disks (M) is at most 22; its worst-case deviation is two when M<94; and its worst-case deviation is four when M <550. In two dimensions, we prove that whenever M is a Fibonacci number, the average performance of the scheme is within 14 percent of the (generally, unachievable) strictly optimal scheme and its worst-case response time is within a multiplicative factor three of the optimal response time for any query, and within a factor 1.5 of the optimal for large queries. We also present comprehensive simulation results, on two-dimensional as well as on higher-dimensional data, that compare and demonstrate the advantages of our scheme over some recently proposed schemes in the literature.