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

Abstract: The Maximum Independent Set (MIS) problem is a well-known NP-complete problem with a wide range of applications across various fields. Heuristic approaches are commonly utilized to efficiently tackle large instances of this problem, yielding high-quality solutions within a reasonable time. However, heuristics face challenges such as falling into local optima and redundant searches within the solution space. This paper introduces an efficient heuristic algorithm for the MIS problem, incorporating two innovative techniques. The first technique features a recurrent evaluation mechanism that monitors the progress of solutions and identifies local optima, triggering restarts to avoid convergence on suboptimal outcomes. The second technique utilizes a sampling-driven inference rule to selectively fix vertices based on sampled solutions, thereby narrowing the search space and enhancing efficiency. Comprehensive experimental evaluations across multiple well-established real-world benchmarks demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in terms of solution quality, computational efficiency, and stability.