Efficient and Local Parallel Random Walks

TL;DR

This paper introduces a new parallel algorithm for computing random walks locally and efficiently, addressing the limitations of previous methods by focusing on small subsets of nodes, which enhances scalability and practical applicability.

Contribution

The paper presents a novel parallel local random walk algorithm that is both memory and round efficient, improving scalability over existing non-local methods.

Findings

The new algorithm is significantly more scalable than previous approaches.

It is both memory-efficient and requires fewer computational rounds.

Experimental results confirm its practical effectiveness in local clustering tasks.

Abstract

Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks has been introduced very recently (Lacki et al.). Unfortunately their method has a fundamental shortcoming: their algorithm is non-local in that it heavily relies on computing random walks out of all nodes in the input graph, even though in many practical applications one is interested in computing random walks only from a small subset of nodes in the graph. In this paper, we present a new algorithm that overcomes this limitation by building random walk efficiently and locally at the same time. We show that our technique is both memory and round efficient, and in particular yields an efficient parallel local clustering algorithm. Finally, we complement our theoretical analysis with experimental results showing that our algorithm is significantly more scalable than previous approaches.