Optimal parallel block access for range queries

Allocation schemes for range queries have been widely used in parallel storage systems to allow fast access to multidimensional data. An allocation scheme distributes data blocks among several devices (e.g. disks) so that the number of parallel block accesses needed per query is minimized. Given a system of k disks, a query that accesses m blocks needs a number of parallel block accesses that is at least OPT = [m/k]. In 2000, Atallah and Prabhakar described an allocation scheme with a guaranteed worst-case performance of OPT + O(log k) parallel block accesses for two dimensions. In this paper, we prove that the scheme of Atallah and Prabhakar has, in fact, guaranteed worst-case performance within an additive constant deviation from OPT: within OPT + 3 parallel block accesses for two dimensions. Also, we identify the type of queries for which the worst-case performance of the scheme is OPT + 1 parallel block accesses.