# Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs

arXiv: https://arxiv.org/abs/1810.10834 · HTML: https://mlsanity.com/paper/1810.10834/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

## Built on by (most cited first, 9 of 9)

- [What's Wrong with Deep Learning in Tree Search for Combinatorial Optimization](https://mlsanity.com/paper/2201.10494/) (2022)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [QAOA Parameter Transferability for Maximum Independent Set using Graph Attention Networks](https://mlsanity.com/paper/2504.21135/) (2025)
- [A Metaheuristic Algorithm for Large Maximum Weight Independent Set Problems](https://mlsanity.com/paper/2203.15805/) (2022)
- [Improved Exact and Heuristic Algorithms for Maximum Weight Clique](https://mlsanity.com/paper/2302.00458/) (2023)
- [On lower bounds of the density of planar periodic sets without unit distances](https://mlsanity.com/paper/2411.13248/) (2024)
- [Dynamic Location Search for Identifying Maximum Weighted Independent Sets in Complex Networks](https://mlsanity.com/paper/2505.04674/) (2025)
- [Distribution-Aware Algorithm Design with LLM Agents](https://mlsanity.com/paper/2605.14141/) (2026)
- [A Fresh Look at Lamarckian Evolution and the Baldwin Effect](https://mlsanity.com/paper/2605.28703/) (2026)

## Abstract (arXiv)

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very effective in practice for unweighted problems, very little is known for weighted problems, in part due to a lack of known effective reductions. In this work, we develop a full suite of new reductions for the maximum weight independent set problem and provide extensive experiments to show their effectiveness in practice on real-world graphs of up to millions of vertices and edges. Our experiments indicate that our approach is able to outperform existing state-of-the-art algorithms, solving many instances that were previously infeasible. In particular, we show that branch-and-reduce is able to solve a large number of instances up to two orders of magnitude faster than existing (inexact) local search algorithms---and is able to solve the majority of instances within 15 minutes. For those instances remaining infeasible, we show that combining kernelization with local search produces higher-quality solutions than local search alone.