{"type":"ScholarlyArticle","title":"Computing (1+epsilon)-Approximate Degeneracy in Sublinear Time","authors":[{"name":"Valerie King","slug":"valerie-king","given":"Valerie","family":"King","affiliation":"University of Victoria , Victoria , Canada"},{"name":"Alex Thomo","slug":"alex-thomo","given":"Alex","family":"Thomo","affiliation":"University of Victoria , Victoria , Canada"},{"name":"Quinton Yong","slug":"quinton-yong","given":"Quinton","family":"Yong","affiliation":"University of Victoria , Victoria , Canada"}],"abstract":"The problem of finding the degeneracy of a graph is a subproblem of the k-core decomposition problem. In this paper, we present a (1 + epsilon)-approximate solution to the degeneracy problem which runs in O(n log n) time, sublinear in the input size for dense graphs, by sampling a small number of neighbors adjacent to high degree nodes. This improves upon the previous work on sublinear approximate degeneracy, which implies a (4 + epsilon)-approximate ~O(n) solution. Our algorithm can be extended to an approximate O(n log n) time solution to the k-core decomposition problem. We also explore the use of our approximate algorithm as a technique for speeding up exact degeneracy computation. We prove theoretical guarantees of our algorithm and provide optimizations, which improve the running time of our algorithm in practice. Experiments on massive real-world web graphs show that our algorithm performs significantly faster than previous methods for computing degeneracy.","doi":"10.24963/ijcai.2023/240","url":"https://ijcai.org/proceedings/2023/240","pdf":"https://ijcai.org/proceedings/2023/0240.pdf","markdown":"https://ijcai.org/proceedings/2023/240.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/240","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":"Data Mining","track":"Main Track","number":240,"pages":{"first":2160,"last":2168},"keywords":["Data Mining: DM: Mining graphs","Multidisciplinary Topics and Applications: MDA: Web and social networks"],"videos":[],"references":[{"position":1,"raw":"[Aamand et al., 2021] Anders Aamand, Adam Karczmarz, Jakub Lacki, Nikos Parotsidis, Peter M. 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