{"type":"ScholarlyArticle","title":"A Game Theoretic Approach For Core Resilience","authors":[{"name":"Sourav Medya","slug":"sourav-medya","given":"Sourav","family":"Medya","affiliation":"Northwestern University"},{"name":"Tiyani Ma","slug":"tiyani-ma","given":"Tiyani","family":"Ma","affiliation":"University of California Los Angeles"},{"name":"Arlei Silva","slug":"arlei-silva","given":"Arlei","family":"Silva","affiliation":"University of California Santa Barbara"},{"name":"Ambuj Singh","slug":"ambuj-singh","given":"Ambuj","family":"Singh","affiliation":"University of California Santa Barbara"}],"abstract":"K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction.  However, k-cores can be quite unstable to network modifications, which motivates the question: How resilient is the k-core structure of a network, such as the Web or Facebook, to edge deletions? We investigate this question from an algorithmic perspective. More specifically, we study the problem of computing a small set of edges for which the removal minimizes the k-core structure of a network. This paper provides a comprehensive characterization of the hardness of the k-core minimization problem (KCM), including innaproximability and parameterized complexity. Motivated by these challenges, we propose a novel algorithm inspired by Shapley value---a cooperative game-theoretic concept--- that is able to leverage the strong interdependencies in the effects of edge removals in the search space. We efficiently approximate Shapley values using a randomized algorithm with probabilistic guarantees. Our experiments, show that the proposed algorithm outperforms competing solutions in terms of k-core minimization while being able to handle large graphs. Moreover, we illustrate how KCM can be applied in the analysis of the k-core resilience of networks.","doi":"10.24963/ijcai.2020/480","url":"https://ijcai.org/proceedings/2020/480","pdf":"https://ijcai.org/proceedings/2020/0480.pdf","markdown":"https://ijcai.org/proceedings/2020/480.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/480","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Multidisciplinary Topics and Applications","track":"Main track","number":480,"pages":{"first":3473,"last":3479},"keywords":["Data Mining: Mining Graphs, Semi Structured Data, Complex Data","Multidisciplinary Topics and Applications: Social Sciences","Data Mining: Theoretical Foundations"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24883/file_24883.m3u8","length_sec":298,"provider":"hls"}],"references":[{"position":1,"raw":"[Adiga and Vullikanti, 2013] Abhijin Adiga and Anil Ku- mar S Vullikanti. 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