{"type":"ScholarlyArticle","title":"An Exact Algorithm for the Minimum Dominating Set Problem","authors":[{"name":"Hua Jiang","slug":"hua-jiang","given":"Hua","family":"Jiang","affiliation":"Engineering Research Center of Cyberspace & School of Software , Yunnan University , China"},{"name":"Zhifei Zheng","slug":"zhifei-zheng","given":"Zhifei","family":"Zheng","affiliation":"Engineering Research Center of Cyberspace & School of Software , Yunnan University , China"}],"abstract":"The Minimum Dominating Set  (MDS) problem is a classic NP-hard combinatorial optimization problem with many practical applications. Solving MDS is extremely challenging in computation. Previous work on exact algorithms mainly focuses on improving the theoretical time complexity and existing practical algorithms for MDS are almost based on heuristic search. In this paper, we propose a novel lower bound and an exact algorithm for MDS. The algorithm implements a branch-and-bound (BnB) approach and employs the new lower bound to reduce search space. Extensive empirical results show that the new lower bound is efficient in  reduction of the search space and the new algorithm is effective for the standard instances and real-world instances. To the best of our knowledge, this is the first effective BnB algorithm for MDS.","doi":"10.24963/ijcai.2023/622","url":"https://ijcai.org/proceedings/2023/622","pdf":"https://ijcai.org/proceedings/2023/0622.pdf","markdown":"https://ijcai.org/proceedings/2023/622.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/622","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":"Search","track":"Main Track","number":622,"pages":{"first":5604,"last":5612},"keywords":["Search: S: Combinatorial search and optimisation","Search: S: Heuristic search"],"videos":[],"references":[{"position":1,"raw":"[Alber et al., 2004] Jochen Alber, Michael R. 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