Parallel Algorithms for Generating Random Networks with Given Degree Sequences

TL;DR

This paper introduces a scalable MPI-based parallel algorithm for generating massive random networks with arbitrary degree distributions, enabling efficient creation of billion-node networks for complex system modeling.

Contribution

The paper presents a novel load-balancing MPI algorithm that efficiently generates large-scale random networks with specified degree sequences, scaling to billions of nodes and edges.

Findings

Achieves $O(rac{m+n}{P}+P)$ runtime with high probability

Uses $O(n)$ space per processor

Generates billion-node networks in one minute with 1024 processors

Abstract

Random networks are widely used for modeling and analyzing complex processes. Many mathematical models have been proposed to capture diverse real-world networks. One of the most important aspects of these models is degree distribution. Chung--Lu (CL) model is a random network model, which can produce networks with any given arbitrary degree distribution. The complex systems we deal with nowadays are growing larger and more diverse than ever. Generating random networks with any given degree distribution consisting of billions of nodes and edges or more has become a necessity, which requires efficient and parallel algorithms. We present an MPI-based distributed memory parallel algorithm for generating massive random networks using CL model, which takes $O(\frac{m+n}{P}+P)$ time with high probability and $O(n)$ space per processor, where $n$, $m$, and $P$ are the number of nodes, edges and processors, respectively. The time efficiency is achieved by using a novel load-balancing algorithm. Our algorithms scale very well to a large number of processors and can generate massive power--law networks with one billion nodes and $250$ billion edges in one minute using $1024$ processors.