# A practical heuristic for finding graph minors

arXiv: https://arxiv.org/abs/1406.2741 · HTML: https://mlsanity.com/paper/1406.2741/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2014.

## Built on by (most cited first, 26 of 26)

- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
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- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Feature Selection for Recommender Systems with Quantum Computing](https://mlsanity.com/paper/2110.05089/) (2021)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [Q-Seg: Quantum Annealing-Based Unsupervised Image Segmentation](https://mlsanity.com/paper/2311.12912/) (2023)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [A Single-Step Multiclass SVM based on Quantum Annealing for Remote Sensing Data Classification](https://mlsanity.com/paper/2303.11705/) (2023)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [CHARME: A chain-based reinforcement learning approach for the minor embedding problem](https://mlsanity.com/paper/2406.07124/) (2024)
- [Quantum-Hybrid Stereo Matching With Nonlinear Regularization and Spatial Pyramids](https://mlsanity.com/paper/2312.16118/) (2023)
- [Scalable Quantum-Inspired Optimization through Dynamic Qubit Compression](https://mlsanity.com/paper/2412.18571/) (2024)
- [Minor Embedding for Quantum Annealing with Reinforcement Learning](https://mlsanity.com/paper/2507.16004/) (2025)
- [GNN-Guided Graph Coarsening and Adaptive QUBO Penalties for the Capacitated Vehicle Routing Problem with Time Windows on a Quantum Annealer](https://mlsanity.com/paper/2609.04593/) (2026)
- [Quantum Deep Learning: Sampling Neural Nets with a Quantum Annealer](https://mlsanity.com/paper/2107.08710/) (2021)
- [Solving Large Break Minimization Problems in a Mirrored Double Round-robin Tournament Using Quantum Annealing](https://mlsanity.com/paper/2110.07239/) (2021)
- [Quantum-Assisted Support Vector Regression](https://mlsanity.com/paper/2111.09304/) (2021)
- [Skipper: Improving the Reach and Fidelity of Quantum Annealers by Skipping Long Chains](https://mlsanity.com/paper/2312.00264/) (2023)
- [Quantum-Classical Sentiment Analysis](https://mlsanity.com/paper/2409.16928/) (2024)
- [Energy Scale Degradation in Sparse Quantum Solvers: A Barrier to Quantum Utility](https://mlsanity.com/paper/2503.08303/) (2025)
- [Addressing the Minor-Embedding Problem in Quantum Annealing and Evaluating State-of-the-Art Algorithm Performance](https://mlsanity.com/paper/2504.13376/) (2025)
- [Infeasibility Aware Large Language Models for Combinatorial Optimization](https://mlsanity.com/paper/2604.01455/) (2026)

## Abstract (arXiv)

We present a heuristic algorithm for finding a graph H as a minor of a graph G that is practical for sparse G and H with hundreds of vertices. We also explain the practical importance of finding graph minors in mapping quadratic pseudo-boolean optimization problems onto an adiabatic quantum annealer.