Learning-Augmented Streaming Algorithms for Approximating MAX-CUT

TL;DR

This paper introduces a learning-augmented streaming algorithm that surpasses the classical 1/2-approximation barrier for MAX-CUT using minimal space by leveraging an oracle with probabilistic accuracy.

Contribution

It presents a novel approach that uses a machine-learned oracle to improve MAX-CUT approximation in streaming models with low space complexity.

Findings

Achieves approximation of 1/2 + Ω(ε^2) with O(poly(1/ε)) space in insertion-only streams.

Extends the approach to fully dynamic streams with poly(1/ε, log n) space.

Surpasses the classical 1/2-approximation barrier using learning-augmented methods.

Abstract

We study learning-augmented streaming algorithms for estimating the value of MAX-CUT in a graph. In the classical streaming model, while a $1/2$-approximation for estimating the value of MAX-CUT can be trivially achieved with $O(1)$ words of space, Kapralov and Krachun [STOC'19] showed that this is essentially the best possible: for any $\epsilon > 0$, any (randomized) single-pass streaming algorithm that achieves an approximation ratio of at least $1/2 + \epsilon$ requires $\Omega(n / 2^{\text{poly}(1/\epsilon)})$ space. We show that it is possible to surpass the $1/2$-approximation barrier using just $O(1)$ words of space by leveraging a (machine learned) oracle. Specifically, we consider streaming algorithms that are equipped with an $\epsilon$-accurate oracle that for each vertex in the graph, returns its correct label in $\{-1, +1\}$, corresponding to an optimal MAX-CUT solution in the graph, with some probability $1/2 + \epsilon$, and the incorrect label otherwise. Within this framework, we present a single-pass algorithm that approximates the value of MAX-CUT to within a factor of $1/2 + \Omega(\epsilon^2)$ with probability at least $2/3$ for insertion-only streams, using only $\text{poly}(1/\epsilon)$ words of space. We also extend our algorithm to fully dynamic streams while maintaining a space complexity of $\text{poly}(1/\epsilon,\log n)$ words.