A Succint Data Structure for Self-indexing Ternary Relations

Sandra Alvarez-Garcia, Guillermo de Bernardo, Nieves Brisaboa, and Gonzalo Navarro

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 k2-tree (ik2-tree), designed to compactly represent and efficiently query general ternary relations. The ik2-tree is an evolution of an existing data structure, the k2-tree, initially designed to represent Web graphs and later applied to other domains. The ik2-tree is able to extend the k2-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 ik2-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 performace with other solutions of the state of the art.