{"type":"ScholarlyArticle","title":"Massively Parallel Single-Source SimRanks in O(log N) Rounds","authors":[{"name":"Siqiang Luo","slug":"siqiang-luo","given":"Siqiang","family":"Luo","affiliation":"Nanyang Technological University"},{"name":"Zulun Zhu","slug":"zulun-zhu","given":"Zulun","family":"Zhu","affiliation":"Nanyang Technological University"}],"abstract":"SimRank is one of the most fundamental measures that evaluate the structural similarity between two nodes in a graph and has been applied in a plethora of data mining and machine learning tasks. These tasks often involve single-source SimRank computation that evaluates the SimRank values between a source node u and all other nodes. Due to its high computation complexity, single-source SimRank computation for large graphs is notoriously challenging, and hence recent studies resort to distributed processing. To our surprise, although SimRank has been widely adopted for two decades, theoretical aspects of distributed SimRanks with provable results have rarely been studied. \r\nIn this paper, we conduct a theoretical study on single-source SimRank computation in the Massive Parallel Computation (MPC) model, which is the standard theoretical framework modeling distributed systems. Existing distributed SimRank algorithms enforce either Ω(log n) communication round complexity or Ω(n) machine space for a graph of n nodes. We overcome this barrier. \r\nParticularly, given a graph of n nodes, for any query node v and constant error ϵ>3/n, we show that using O(log² log n) rounds of communication among machines is enough to compute single-source SimRank values with at most ϵ absolute errors, while each machine only needs a space sub-linear to n. To the best of our knowledge, this is the first single-source SimRank algorithm in MPC that can overcome the Θ(log n) round complexity barrier with provable result accuracy.","doi":"10.24963/ijcai.2024/249","url":"https://ijcai.org/proceedings/2024/249","pdf":"https://ijcai.org/proceedings/2024/0249.pdf","markdown":"https://ijcai.org/proceedings/2024/249.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/249","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Data Mining","track":"Main Track","number":249,"pages":{"first":2252,"last":2260},"keywords":["Data Mining: DM: Parallel, distributed and cloud-based high performance mining","Data Mining: DM: Theoretical foundations of data mining"],"videos":[],"references":[{"position":1,"raw":"[Antonellis et al., 2008] Ioannis Antonellis, Hector Garcia- Molina, and Chi-Chao Chang. 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