# A Bregman-Sinkhorn Algorithm for the Maximum Weight Independent Set Problem

arXiv: https://arxiv.org/abs/2408.02086 · HTML: https://mlsanity.com/paper/2408.02086/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS](https://mlsanity.com/paper/2605.05330/) (2026)

## Abstract (arXiv)

We propose a scalable approximate algorithm for the NP-hard maximum-weight independent set problem, based on dual coordinate descent applied to a smoothed clique-cover LP relaxation. Our method, a variant of the Bregman/Sinkhorn algorithm, employs entropy smoothing with a novel duality-gap-based smoothing scheduling strategy that empirically outperforms standard feasibility scheduling for the relaxed problem. Our new projection to the primal feasible set enables accurate duality gap estimation. Combined with a basic primal heuristic leveraging reduced costs, our approach yields high-quality integer solutions. On real-world datasets, it efficiently finds high-quality approximate solutions for graphs with up to 882,000 nodes and 344 million edges within seconds.