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

TL;DR

This survey reviews and consolidates various data reduction rules for the NP-hard Maximum Weight Independent Set problem, highlighting their role in simplifying instances for more efficient exact and heuristic solutions.

Contribution

It provides a comprehensive overview and a reference implementation of data reduction rules for MWIS, serving as a centralized resource for future research.

Findings

Data reduction rules significantly improve problem-solving efficiency.

The survey includes a reference implementation of reduction techniques.

Reductions enable solving larger MWIS instances more effectively.

Abstract

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.