Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

TL;DR

This paper introduces a novel sampling algorithm that significantly improves the efficiency of simulating spreading processes on complex networks, reducing computational complexity from polynomial to nearly logarithmic scale.

Contribution

The authors develop a composition and rejection sampling method that achieves near-logarithmic complexity for network simulations, addressing limitations of existing algorithms.

Findings

Existing algorithms scale polynomially on dense or heterogeneous networks.

The proposed method achieves an average-case complexity of O[log(log N)] per update.

The approach is adaptable to both Markovian and non-Markovian dynamics.

Abstract

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require $\mathcal{O}(\log N)$ or even $\mathcal{O}(1)$ operations per update---where $N$ is the number of nodes---display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of $\mathcal{O} [\log(\log N)]$ per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.