A succinct data structure for self-indexing ternary relations

TL;DR

This paper introduces the I$K^2$-tree, a novel compressed data structure that efficiently represents and queries ternary relations, extending the $K^2$-tree to handle three-dimensional data for applications like RDF and Temporal Graphs.

Contribution

It presents the I$K^2$-tree, a new self-indexed data structure for ternary relations, extending the $K^2$-tree to support three-dimensional data with efficient querying capabilities.

Findings

I$K^2$-tree reduces space usage compared to existing solutions.

It provides efficient query performance for ternary relations.

Experimental results demonstrate its effectiveness in real-world domains.

Abstract

The representation of binary relations has been intensively studied and many different theoretical and practical representations have been proposed to answer the usual queries in multiple domains. However, ternary relations have not received as much attention, even though many real-world applications require the processing of ternary relations. In this paper we present a new compressed and self-indexed data structure that we call Interleaved $K^2$-tree (I$K^2$-tree), designed to compactly represent and efficiently query general ternary relations. The I$K^2$-tree is an evolution of an existing data structure, the $K^2$-tree, initially designed to represent Web graphs and later applied to other domains. The I$K^2$-tree is able to extend the $K^2$-tree to represent a ternary relation, based on the idea of decomposing it into a collection of binary relations but providing indexing capabilities in all the three dimensions. We present different ways to use I$K^2$-tree to model different types of ternary relations using as reference two typical domains: RDF and Temporal Graphs. We also experimentally evaluate our representations comparing them in space usage and performance with other solutions of the state of the art.