{"type":"ScholarlyArticle","title":"A Fast Maximum k-Plex Algorithm Parameterized by the Degeneracy Gap","authors":[{"name":"Zhengren Wang","slug":"zhengren-wang","given":"Zhengren","family":"Wang","affiliation":"University of Electronic Science and Technology of China"},{"name":"Yi Zhou","slug":"yi-zhou","given":"Yi","family":"Zhou","affiliation":"University of Electronic Science and Technology of China"},{"name":"Chunyu Luo","slug":"chunyu-luo","given":"Chunyu","family":"Luo","affiliation":"University of Electronic Science and Technology of China"},{"name":"Mingyu Xiao","slug":"mingyu-xiao","given":"Mingyu","family":"Xiao","affiliation":"University of Electronic Science and Technology of China"}],"abstract":"Given a graph, the k-plex is a vertex set in which each vertex is not adjacent to at most k-1 other vertices in the set. The maximum k-plex problem, which asks for the largest k-plex from a given graph, is an important but computationally challenging problem in applications like graph search and community detection.  So far, there is a number of empirical algorithms  without sufficient theoretical explanations on the efficiency. We try to bridge this gap by defining a novel parameter of the input instance, g_k(G), the gap between the degeneracy bound and the size of maximum k-plex in the given graph, and presenting an exact algorithm parameterized by g_k(G). In other words, we design an algorithm with running time polynomial in the size of input graph and exponential in g_k(G) where k is a constant. Usually, g_k(G) is small and bounded by O(log(|V|)) in real-world graphs, indicating that the algorithm runs in polynomial time. We also carry out massive experiments and show that the algorithm is competitive with the state-of-the-art solvers. Additionally, for large k values such as 15 and 20, our algorithm has superior performance over existing algorithms.","doi":"10.24963/ijcai.2023/627","url":"https://ijcai.org/proceedings/2023/627","pdf":"https://ijcai.org/proceedings/2023/0627.pdf","markdown":"https://ijcai.org/proceedings/2023/627.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/627","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":627,"pages":{"first":5648,"last":5656},"keywords":["Search: S: Combinatorial search and optimisation","Search: S: Heuristic search"],"videos":[],"references":[{"position":1,"raw":"[Balasundaram et al., 2011] Balabhaskar Balasundaram, Sergiy Butenko, and Illya V Hicks. 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