Triangle and Four Cycle Counting with Predictions in Graph Streams

TL;DR

This paper introduces data-driven streaming algorithms utilizing a 'heavy edge' oracle to efficiently estimate triangles and four cycles in graph streams, improving space bounds and robustness to noise compared to classical methods.

Contribution

It develops novel one-pass streaming algorithms with oracle assistance for triangle and four cycle counting, expanding the capabilities of classical graph stream algorithms.

Findings

Algorithms outperform previous bounds in space efficiency.

Performance remains robust under various noise models.

Experimental results favor the proposed methods over existing algorithms.

Abstract

We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, (Hsu 2018) and (Jiang 2020) applied machine learning techniques in other data stream problems, using a trained oracle that can predict certain properties of the stream elements to improve on prior "classical" algorithms that did not use oracles. In this paper, we explore the power of a "heavy edge" oracle in multiple graph edge streaming models. In the adjacency list model, we present a one-pass triangle counting algorithm improving upon the previous space upper bounds without such an oracle. In the arbitrary order model, we present algorithms for both triangle and four cycle estimation with fewer passes and the same space complexity as in previous algorithms, and we show several of these bounds are optimal. We analyze our algorithms under several noise models, showing that the algorithms perform well even when the oracle errs. Our methodology expands upon prior work on "classical" streaming algorithms, as previous multi-pass and random order streaming algorithms can be seen as special cases of our algorithms, where the first pass or random order was used to implement the heavy edge oracle. Lastly, our experiments demonstrate advantages of the proposed method compared to state-of-the-art streaming algorithms.