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Conference

Beyond Uniformity in Combinatorial Streams: Sparsity-Adaptive and Adversarially Robust Oracles for MAX-CUT Approximation

Aug 2026 · International Conference Computational Vision and Bio Inspired Computing · pp. 41-47 · 0 citations · 30 references

Abstract

Recent advances in learning-augmented streaming show that access to an $\epsilon$-accurate oracle enables single-pass sublinear-space algorithms to surpass the classical 1/2 approximation barrier for MAX-CUT, achieving guarantees of $1 / 2+\Omega\left(\epsilon^{2}\right)$. However, existing formulations implicitly assume uniform oracle accuracy, benign stream orderings, and stationarity, limiting applicability to real-world graph streams exhibiting heavy-tailed sparsity, adversarial reordering, and temporal drift. This paper introduces a unified framework with three components: a Sparsity-Adaptive Hierarchical Oracle (SAHO), an Adversarially Robust Stream Processing (ARSP) mechanism, and a Temporal Community-Aware Oracle (TCAO). Theoretical analysis establishes that the framework generalizes uniformoracle learning-augmented streaming. Empirical evaluations on heavy-tailed communication networks and bounded-degree spatial graphs confirm consistent gains over uniform baselines while matching classical greedy guarantees when oracle information provides no marginal benefit.

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