This paper addresses the query performance issue for Relational OLAP (ROLAP) datacubes. We present RCUBE, a distributed multi-dimensional ROLAP indexing scheme which is practical to implement, requires only a small communication volume, and is fully adapted to distributed disks. Our solution is efficient for spatial searches in high dimensions and scalable in terms of data sizes, dimensions, and number of processors. Our method is also incrementally maintainable. Using “surrogate ” group-bys, it allows for the efficient processing of arbitrary OLAP queries on partial cubes, where not all of the group-bys have been materialized. Our experiments with RCUBE show that the ROLAP advantage of better scalability, in comparison to MOLAP, can be maintained while providing, at the same time, a fast and flexible index for OLAP queries.

Many applications use sequences of n consecutive symbols (n-grams). We review n-gram hashing and prove that recursive hash families are pairwise independent at best. We prove that hashing by irreducible polynomials is pairwise independent whereas hashing by cyclic polynomials is quasi-pairwise independent: we make it pairwise independent by discarding n − 1 bits. One application of hashing is to estimate the number of distinct n-grams, a view-size estimation problem. While view sizes can be estimated by sampling under statistical assumptions, we desire a statistically unassuming algorithm with universally valid accuracy bounds. Most related work has focused on repeatedly hashing the data, which is prohibitive for large data sources. We prove that a one-pass onehash algorithm is sufficient for accurate estimates if the hashing is sufficiently independent. For example, we can improve by a factor of 2 the theoretical bounds on estimation accuracy by replacing pairwise independent hashing by 4-wise independent hashing. We show that recursive random hashing is sufficiently independent in practice. Maybe surprisingly, our experiments showed that hashing by cyclic polynomials, which is only quasi-pairwise independent, sometimes outperformed 10-wise independent hashing while being twice as fast. For comparison, we measured the time to obtain exact n-gram counts using suffix arrays and show that, while we used hardly any storage, we were an order of magnitude faster. The experiments used a large collection of English text from Project Gutenberg as well as synthetic data.