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The Maximum Independent Set (MIS) problem is a well-known NP-complete problemwith a wide range of applications across various fields. Heuristic approachesare commonly utilized to efficiently tackle large instances of this problem,yielding high-quality solutions within a reasonable time. However, heuristicsface challenges such as falling into local optima and redundant searches withinthe solution space. This paper introduces an efficient heuristic algorithm forthe MIS problem, incorporating two innovative techniques. The first techniquefeatures a recurrent evaluation mechanism that monitors the progress ofsolutions and identifies local optima, triggering restarts to avoid convergenceon suboptimal outcomes. The second technique utilizes a sampling-driveninference rule to selectively fix vertices based on sampled solutions, therebynarrowing the search space and enhancing efficiency. Comprehensive experimentalevaluations across multiple well-established real-world benchmarks demonstratethat the proposed algorithm outperforms state-of-the-art algorithms in terms ofsolution quality, computational efficiency, and stability.

ARES: An Efficient Algorithm with Recurrent Evaluation and Sampling-Driven Inference for Maximum Independent Set