# Efficient Representation of Multidimensional Data over Hierarchical Domains

arXiv: https://arxiv.org/abs/1612.04094 · HTML: https://mlsanity.com/paper/1612.04094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2016.

## Built on by (most cited first, 1 of 1)

- [Machine Learning and Data Analysis Using Posets: A Survey](https://mlsanity.com/paper/2404.03082/) (2024)

## Abstract (arXiv)

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 k2-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.