Efficient Representation of Multidimensional Data over Hierarchical Domains

TL;DR

This paper introduces a hierarchical domain-aware data structure for efficient multidimensional data representation and query processing in OLAP systems, improving over generic methods by leveraging domain hierarchies.

Contribution

It proposes a novel hierarchical partitioning approach that organizes data according to domain hierarchies, enabling more efficient query resolution than generic multidimensional structures.

Findings

More efficient query resolution due to fewer nodes accessed.

Compact data representation tailored to hierarchical domains.

Significant performance improvements over generic methods.

Abstract

We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the typical case of OLAP databases. A basic approach is to represent each hierarchy as a one-dimensional line and recast the queries as multidimensional range queries. This approach can be implemented compactly by generalizing to more dimensions the $k^2$-treap, a compact representation of two-dimensional points that allows for efficient summarization queries along generic ranges. Instead, we propose a more flexible generalization, which instead of a generic quadtree-like partition of the space, follows the domain hierarchies across each dimension to organize the partitioning. The resulting structure is much more efficient than a generic multidimensional structure, since queries are resolved by aggregating much fewer nodes of the tree.