PUBO Formulation for MST and Application to Optimum-Path Forest
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Quantum Physics arXiv:2605.20637 (quant-ph) [Submitted on 20 May 2026] Title:PUBO Formulation for MST and Application to Optimum-Path Forest Authors:Guilherme E. L. Pexe, Lucas A. M. Rattighieri, Leandro A. Passos, Danilo S. Jodas, Douglas Rodrigues, Felipe F. Fanchini, João P. Papa, Kelton A. P. Costa View a PDF of the paper titled PUBO Formulation for MST and Application to Optimum-Path Forest, by Guilherme E. L. Pexe and 7 other authors View PDF HTML (experimental) Abstract:The Optimum-Path Forest is a graph-based framework for designing classifiers that exploit inter-sample connectivity. A particular variant constructs decision boundaries based on prototypes computed by a Minimum Spanning Tree (MST) over the training data, which might become prohibitive for large-scale datasets. In this context, Quantum Machine Learning has emerged as a promising approach to overcome the high computational burden of combinatorial problems. We propose a quantum-inspired approach for prototype selection in OPF classifiers by reformulating the MST problem as a Polynomial Unconstrained Binary Optimization (PUBO) task and further employing the Feedback-Based Quantum Optimization (FALQON) algorithm for Hamiltonian minimization. The PUBO formulation reduces the need for qubits and eliminates the need for auxiliary variables, thereby addressing scalability constraints in current quantum hardware. Experiments on real-world datasets demonstrate that the FALQON-optimized MST achieves accuracies comparable to those of the classical Prim's algorithm while maintaining prototype quality. While FALQON occasionally reached local minima, it did not significantly impact the accuracy of the prototype selection process. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.20637 [quant-ph] (or arXiv:2605.20637v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.20637 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Guilherme Pexe [view email] [v1] Wed, 20 May 2026 02:46:56 UTC (222 KB) Full-text links: Access Paper: View a PDF of the paper titled PUBO Formulation for MST and Application to Optimum-Path Forest, by Guilherme E. L. Pexe and 7 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)