{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T07:15:29Z","timestamp":1779174929345,"version":"3.51.4"},"reference-count":55,"publisher":"Association for Computing Machinery (ACM)","issue":"10","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. VLDB Endow."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p>\n            Directed graphs are prevalent in social networks, web networks, and communication networks. A well-known concept of the directed graph is the D-core, or (\n            <jats:italic>k, l<\/jats:italic>\n            )-core, which is the maximal subgraph in which each vertex has an in-degree not less than\n            <jats:italic>k<\/jats:italic>\n            and an out-degree not less than\n            <jats:italic>l.<\/jats:italic>\n            Computing the non-empty D-cores for all possible values of\n            <jats:italic>k<\/jats:italic>\n            and\n            <jats:italic>l<\/jats:italic>\n            , a.k.a. D-core decomposition, has found versatile applications spanning social network analysis, community search, and graph visualization. However, existing algorithms of D-core decomposition suffer from efficiency and scalability issues on large graphs, because serial peeling-based algorithms are limited by single-core utilization, while skyline coreness-based methods exhibit notably high time complexity. To tackle these issues, in this paper, we propose efficient parallel algorithms for D-core decomposition by leveraging the computational prowess of multicore CPUs. Specifically, we first propose a novel algorithm that computes the D-cores for each possible\n            <jats:italic>k<\/jats:italic>\n            value, by exploiting an implicit level-by-level vertex removal strategy, which not only diminishes dependencies between vertices but also maintains a time complexity akin to that of sequential algorithms. We further develop an advanced algorithm by introducing a novel concept of D-shell, which allows us to curtail redundant computations by reducing the necessary\n            <jats:italic>k<\/jats:italic>\n            values when computing corresponding D-cores, and deriving D-cores with larger\n            <jats:italic>k<\/jats:italic>\n            values from the D-cores currently computed based on D-shell. Extensive experiments on ten real-world large graphs show that our algorithms are highly efficient and scalable, and the advanced algorithm is up to two orders of magnitude faster than the state-of-the-art parallel decomposition algorithm with 32 threads.\n          <\/jats:p>","DOI":"10.14778\/3675034.3675054","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T22:19:11Z","timestamp":1722982751000},"page":"2654-2667","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Efficient Parallel D-Core Decomposition at Scale"],"prefix":"10.14778","volume":"17","author":[{"given":"Wensheng","family":"Luo","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yixiang","family":"Fang","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunxu","family":"Lin","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingli","family":"Zhou","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,8,6]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Large scale networks fingerprinting and visualization using the k-core decomposition. 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