{"type":"ScholarlyArticle","title":"Solving Quantum-Inspired Perfect Matching Problems via Tutte-Theorem-Based Hybrid Boolean Constraints","authors":[{"name":"Moshe Y. Vardi","slug":"moshe-y-vardi","given":"Moshe Y.","family":"Vardi","affiliation":"Rice University , Houston , TX , USA"},{"name":"Zhiwei Zhang","slug":"zhiwei-zhang","given":"Zhiwei","family":"Zhang","affiliation":"Rice University , Houston , TX , USA"}],"abstract":"Determining the satisfiability of Boolean constraint-satisfaction problems with different types of constraints, that is hybrid constraints,  is a well-studied problem with important applications. We study a new application of hybrid Boolean constraints, which arises in quantum computing. The problem relates to constrained perfect matching in edge-colored graphs. While general-purpose hybrid constraint solvers can be powerful, we show that direct encodings of the constrained-matching problem as hybrid constraints scale poorly and special techniques are still needed. We propose a novel encoding based on Tutte's Theorem in graph theory as well as optimization techniques. Empirical results demonstrate that our encoding, in suitable languages with advanced SAT solvers, scales significantly better than a number of competing approaches on constrained-matching benchmarks. Our study identifies the necessity of designing problem-specific encodings when applying powerful general-purpose constraint solvers.","doi":"10.24963/ijcai.2023/227","url":"https://ijcai.org/proceedings/2023/227","pdf":"https://ijcai.org/proceedings/2023/0227.pdf","markdown":"https://ijcai.org/proceedings/2023/227.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/227","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":227,"pages":{"first":2039,"last":2048},"keywords":["Constraint Satisfaction and Optimization: CSO: Applications","Constraint Satisfaction and Optimization: CSO: Constraint satisfaction","Constraint Satisfaction and Optimization: CSO: Modeling"],"videos":[],"references":[{"position":1,"raw":"[Aloul et al., 2006] Fadi A Aloul, Karem A Sakallah, and Igor L Markov. 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