{"type":"ScholarlyArticle","title":"Fine-grained Complexity of Partial Minimum Satisfiability","authors":[{"name":"Ivan Bliznets","slug":"ivan-bliznets","given":"Ivan","family":"Bliznets","affiliation":"HSE University , St.Petersburg , Russia; St. Petersburg Department of Steklov Mathematical Institute of"},{"name":"Danil Sagunov","slug":"danil-sagunov","given":"Danil","family":"Sagunov","affiliation":"St. Petersburg Department of Steklov Mathematical Institute of"},{"name":"Kirill Simonov","slug":"kirill-simonov","given":"Kirill","family":"Simonov","affiliation":"Algorithms and Complexity Group , TU Wien , Austria; Russian Academy of Sciences , St.Petersburg , Russia"}],"abstract":"There is a well-known approach to cope with NP-hard problems in practice: reduce the given problem to SAT or MAXSAT and run a SAT or a MaxSAT solver. This method is very efficient since SAT/MaxSAT solvers are extremely well-studied, as well as the complexity of these problems. At AAAI 2011, Li et al. proposed an alternative to this approach and suggested the Partial Minimum Satisfiability problem as a reduction target for NP-hard problems. They developed the MinSatz solver and showed that reducing to Partial Minimum Satisfiability and using MinSatz is in some cases more efficient than reductions to SAT or MaxSAT. Since then many results connected to the Partial Minimum Satisfiability problem were published. However, to the best of our knowledge, the worst-case complexity of Partial Minimum Satisfiability has not been studied up until now.  Our goal is to fix the issue and show a O*((2-ɛ)^m) lower bound under the SETH assumption (here m is the total number of clauses), as well as several other lower bounds and parameterized exact algorithms with better-than-trivial running time.","doi":"10.24963/ijcai.2022/247","url":"https://ijcai.org/proceedings/2022/247","pdf":"https://ijcai.org/proceedings/2022/0247.pdf","markdown":"https://ijcai.org/proceedings/2022/247.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/247","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":247,"pages":{"first":1774,"last":1780},"keywords":["Constraint Satisfaction and Optimization: Constraint Satisfaction","Constraint Satisfaction and Optimization: Constraint Optimization","Constraint Satisfaction and Optimization: Satisfiabilty"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986823","length_sec":85,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984966","length_sec":356,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Abramé and Habet, 2015] André Abramé and Djamal Ha- bet. 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