Faster Dynamic Compressed d-ary Relations

TL;DR

This paper introduces a faster dynamic compressed d-ary relation structure by reinterpreting the $k^d$-tree as a dynamic trie on Morton codes, surpassing previous bitvector-based methods in efficiency.

Contribution

It proposes a novel interpretation of the $k^d$-tree as a dynamic trie on Morton codes, achieving improved operation times over traditional bitvector approaches.

Findings

Operation times are below the lower bound of dynamic bitvectors.

The new approach offers better practical performance.

It effectively handles sparse and clustered data in multiple dimensions.

Abstract

The $k^2$-tree is a successful compact representation of binary relations that exhibit sparseness and/or clustering properties. It can be extended to $d$ dimensions, where it is called a $k^d$-tree. The representation boils down to a long bitvector. We show that interpreting the $k^d$-tree as a dynamic trie on the Morton codes of the points, instead of as a dynamic representation of the bitvector as done in previous work, yields operation times that are below the lower bound of dynamic bitvectors and offers improved time performance in practice.