Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades

TL;DR

This paper introduces efficient algorithms for graph randomisation using Curveball trades, demonstrating that global trades converge uniformly and outperform traditional methods in speed while maintaining quality.

Contribution

It presents the first I/O-efficient Curveball algorithms and shows that global trades can be performed efficiently, achieving faster convergence and better performance than existing methods.

Findings

Global trades converge to a uniform distribution.

EM-PGCB is nearly ten times faster than ESMC.

New algorithms improve efficiency of graph randomisation.

Abstract

Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved. Curveball is a novel approach that instead considers the whole neighbourhoods of randomly drawn node pairs. Its Markov chain converges to a uniform distribution, and experiments suggest that it requires less steps than the established ESMC. Since trades however are more expensive, we study Curveball's practical runtime by introducing the first efficient Curveball algorithms: the I/O-efficient EM-CB for simple undirected graphs and its internal memory pendant IM-CB. Further, we investigate global trades processing every node in a graph during a single super step, and show that undirected global trades converge to a uniform distribution and perform superior in practice. We then discuss EM-GCB and EM-PGCB for global trades and give experimental evidence that EM-PGCB achieves the quality of the state-of-the-art ESMC algorithm EM-ES nearly one order of magnitude faster.