Near Uniform Triangle Sampling Over Adjacency List Graph Streams

TL;DR

This paper introduces efficient streaming algorithms for approximately sampling triangles uniformly in adjacency list graph streams, matching space complexities of triangle counting algorithms, and extends results to vertex and edge models.

Contribution

It presents the first algorithms for near-uniform triangle sampling in adjacency list streams with space complexity comparable to counting algorithms.

Findings

Algorithms achieve near-uniform triangle sampling in adjacency list streams.

Space complexity matches that of triangle counting algorithms.

Results extend to vertex and edge arrival models.

Abstract

Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater attention in the literature than the sampling variant. In this work, we consider the problem of approximately sampling triangles in different models of streaming with the focus being on the adjacency list model. In this problem, the edges of a graph $G$ will arrive over a data stream. The goal is to design efficient streaming algorithms that can sample and output a triangle from a distribution, over the triangles in $G$, that is close to the uniform distribution over the triangles in $G$. The distance between distributions is measured in terms of $\ell_1$-distance. The main technical contribution of this paper is to design algorithms for this triangle sampling problem in the adjacency list model with the space complexities matching their counting variants. For the sake of completeness, we also show results on the vertex and edge arrival models.