A Comprehensive Survey of Data Reduction Rules for the Maximum Weighted Independent Set Problem

The Maximum Weight Independent Set (MWIS) problem, as well as its related problems such as Minimum Weight Vertex Cover, are fundamental NP-hard problems with numerous practical applications. Due to their computational complexity, a variety of data reduction rules have been proposed in recent years to simplify instances of these problems, enabling exact solvers and heuristics to handle them more effectively. Data reduction rules are polynomial time procedures that can reduce an instance while ensuring that an optimal solution on the reduced instance can be easily extended to an optimal solution for the original instance. Data reduction rules have proven to be especially useful in branch-and-reduce methods, where successful reductions often lead to problem instances that can be solved exactly. This survey provides a comprehensive overview of data reduction rules for the MWIS problem. We also provide a reference implementation for these reductions. This survey will be updated as new reduction techniques are developed, serving as a centralized resource for researchers and practitioners.