{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T04:58:51Z","timestamp":1781326731523,"version":"3.54.1"},"reference-count":85,"publisher":"Association for Computing Machinery (ACM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. ACM Manag. Data"],"published-print":{"date-parts":[[2025,12,4]]},"abstract":"<jats:p>\n                    Given a directed graph\n                    <jats:italic toggle=\"yes\">G<\/jats:italic>\n                    , the directed densest subgraph (DDS) problem refers to finding a subgraph from\n                    <jats:italic toggle=\"yes\">G<\/jats:italic>\n                    , whose density is the highest among all subgraphs of\n                    <jats:italic toggle=\"yes\">G<\/jats:italic>\n                    . The DDS problem is fundamental to a wide range of applications, such as fake follower detection and community mining. However, existing DDS solutions often incur significant redundant computations and have weaker theoretical guarantees. To tackle these issues, we present both practically and theoretically efficient DDS discovery algorithms (including both approximation and exact methods) in this paper. Specifically, we first introduce a novel graph reduction technique that locates the DDS into a highly smaller subgraph, with non-trivial theoretical guarantees. We further develop an efficient approximation algorithm by employing\n                    <jats:italic toggle=\"yes\">gradient projection<\/jats:italic>\n                    and theoretically prove that it requires fewer iterations to achieve the same solution accuracy compared to state-of-the-art approximation DDS algorithms. Finally, we propose an efficient exact algorithm based on this novel approximation algorithm. We have performed an extensive empirical evaluation of our approaches on 15 real and 8 synthetic large datasets. The results show that our proposed algorithms are up to two orders of magnitude faster than the state-of-the-art.\n                  <\/jats:p>","DOI":"10.1145\/3769785","type":"journal-article","created":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T04:32:13Z","timestamp":1764995533000},"page":"1-27","source":"Crossref","is-referenced-by-count":2,"title":["Efficient and Scalable Directed Densest Subgraph Discovery"],"prefix":"10.1145","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-5630-6822","authenticated-orcid":false,"given":"Yingli","family":"Zhou","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3669-0022","authenticated-orcid":false,"given":"Luocheng","family":"Liang","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5047-8593","authenticated-orcid":false,"given":"Yixiang","family":"Fang","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,12,5]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Diameter of the world-wide web. nature","author":"Albert R\u00e9ka","year":"1999","unstructured":"R\u00e9ka Albert, Hawoong Jeong, and Albert-L\u00e1szl\u00f3 Barab\u00e1si. 1999. 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