An Adaptive Repeated-Intersection-Reduction Local Search for the Maximum Independent Set Problem

The maximum independent set (MIS) problem, a classical NP-hard problem with extensive applications in various areas, aims to find the largest set of vertices with no edge among them. Due to its computational intractability, it is difficult to solve the MIS problem effectively, especially on large graphs. Employing heuristic approaches to obtain a good solution within an acceptable amount of time has attracted much attention in literature. In this paper, we propose an efficient local search framework for MIS called ARIR, which encompasses two main parts: a lightweight adaptive mechanism and a novel inexact efficient reduction rule to simplify instances. Based on ARIR, three algorithms -- ARIR-I, ARIR-II, and ARIR-III -- are developed by adopting three distinct reduction strategies. We conduct experiments on five benchmarks, encompassing 92 instances. Compared with six state-of-the-art algorithms, our ARIR-based algorithms offer the best accuracy on the majority of instances, while obtaining competitive results on the remaining instances.