{"type":"ScholarlyArticle","title":"A Strengthened Branch and Bound Algorithm for the Maximum Common (Connected) Subgraph Problem","authors":[{"name":"Jianrong Zhou","slug":"jianrong-zhou","given":"Jianrong","family":"Zhou","affiliation":"School of Computer Science and Technology , Huazhong University of Science and Technology"},{"name":"Kun He","slug":"kun-he","given":"Kun","family":"He","affiliation":"School of Computer Science and Technology , Huazhong University of Science and Technology"},{"name":"Jiongzhi Zheng","slug":"jiongzhi-zheng","given":"Jiongzhi","family":"Zheng","affiliation":"School of Computer Science and Technology , Huazhong University of Science and Technology"},{"name":"Chu-Min Li","slug":"chu-min-li","given":"Chu-Min","family":"Li","affiliation":"MIS , University of Picardie Jules Verne , France"},{"name":"Yanli Liu","slug":"yanli-liu","given":"Yanli","family":"Liu","affiliation":"WuHan University of Science and Technology , China"}],"abstract":"We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which we search for the maximum common (connected) induced subgraph, the first operator of LSM maintains a score for the branching node using the short-term reward of each vertex of the first graph and the long-term reward of each vertex pair of the two graphs. In this way, the BnB process learns to reduce the search tree size significantly and boost the algorithm performance. The second operator of LUM further improves the performance by simultaneously matching the leaf vertices connected to the current matched vertices, and allows the algorithm to match multiple vertex pairs without affecting the optimality of solution. We incorporate the two operators into the state-of-the-art BnB algorithm McSplit, and denote the resulting algorithm as McSplit+LL. Experiments show that McSplit+LL outperforms McSplit+RL, a more recent variant of McSplit using reinforcement learning that is superior than McSplit.","doi":"10.24963/ijcai.2022/265","url":"https://ijcai.org/proceedings/2022/265","pdf":"https://ijcai.org/proceedings/2022/0265.pdf","markdown":"https://ijcai.org/proceedings/2022/265.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/265","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":265,"pages":{"first":1908,"last":1914},"keywords":["Constraint Satisfaction and Optimization: Solvers and Tools","Constraint Satisfaction and Optimization: Constraint Optimization"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986804","length_sec":42,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984947","length_sec":233,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Bahiense et al., 2012] Laura Bahiense, Gordana Manić, Breno Piva, and Cid C De Souza. 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