Compressed Representation of Dynamic Binary Relations with Applications

TL;DR

This paper presents a dynamic data structure based on a variant of the k^2-tree for efficiently representing and updating binary relations, with applications to Web graphs and RDF databases, achieving high compression and fast queries.

Contribution

It introduces a novel dynamic variant of the k^2-tree that supports efficient updates and queries in binary relation representations, extending static compression techniques.

Findings

Achieves compression ratios close to static structures.

Supports efficient insertion and deletion of pairs.

Provides fast query times comparable to static counterparts.

Abstract

We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of clustering in the binary relation to achieve compression. Our structure can efficiently check whether two objects $(a,b) \in A \times B$ are related, and list the objects of $B$ related to some $a \in A$ and vice versa. Additionally, our structure allows inserting and deleting pairs $(a,b)$ in the relation, as well as modifying the base sets $A$ and $B$. We test our dynamic data structure in different contexts, including the representation of Web graphs and RDF databases. Our experiments show that our dynamic data structure achieves good compression ratios and fast query times, close to those of a static representation, while also providing efficient support for updates in the represented binary relation.