On dynamic succinct graph representations

TL;DR

This paper proposes a new dynamic graph representation using $k^2$-trees, leveraging dynamic bit vectors, and demonstrates its practical competitiveness through experiments.

Contribution

It introduces an alternative implementation for dynamic graphs with $k^2$-trees, extending their use beyond static graph representation.

Findings

The new implementation is practically competitive.

It effectively uses dynamic bit vectors.

Experimental results validate the approach.

Abstract

We address the problem of representing dynamic graphs using $k^2$-trees. The $k^2$-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact representations of bit vectors. Hence, by relying on compact representations of dynamic bit vectors, we can also represent dynamic graphs. In this paper we follow instead the ideas by Munro {\em et al.}, and we present an alternative implementation for representing dynamic graphs using $k^2$-trees. Our experimental results show that this new implementation is competitive in practice.