# Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons

arXiv: https://arxiv.org/abs/2412.16181 · HTML: https://mlsanity.com/paper/2412.16181/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 6 of 6)

- [Simple, Robust and Optimal Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1512.08949/) (2015)
- [Optimal Full Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2101.08421/) (2021)
- [Spectral Ranking using Seriation](https://mlsanity.com/paper/1406.5370/) (2014)
- [Tight Localizations of Feedback Sets](https://mlsanity.com/paper/2001.01440/) (2020)
- [Vertex Ordering Problems in Directed Graph Streams](https://mlsanity.com/paper/2105.08215/) (2021)
- [Cross-Document Neural Re-Ranking via Query-Induced Subgraphs](https://mlsanity.com/paper/2406.11720/) (2024)

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

- [Feedforward Ordering in Neural Connectomes via Feedback Arc Minimization](https://mlsanity.com/paper/2506.13799/) (2025)

## Abstract (arXiv)

The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using learning based methods, but did not examine the underlying connection to MWFAS. In this paper, we investigate this relationship and introduce efficient combinatorial algorithms for solving MWFAS as a means of addressing the ranking problem. Our experimental results show that these simple, learning free methods achieve substantially faster runtimes than recent learning based approaches, while also delivering competitive, and in many cases superior, ranking accuracy. These findings suggest that lightweight combinatorial techniques offer a scalable and effective alternative to deep learning for large scale ranking tasks.