{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T03:06:09Z","timestamp":1787022369726,"version":"3.56.0"},"reference-count":60,"publisher":"Association for Computing Machinery (ACM)","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. VLDB Endow."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p>\n                    As one of the most fundamental problems in graph data mining, the\n                    <jats:italic>densest subgraph discovery<\/jats:italic>\n                    (DSD) problem has found a broad spectrum of real applications, such as social network community detection, graph index construction, regulatory motif discovery in DNA, fake follower detection, and so on. Theoretically, DSD closely relates to other fundamental graph problems, such as network flow and bipartite matching. Triggered by these applications and connections, DSD has garnered much attention from the database, data mining, theory, and network communities.\n                  <\/jats:p>\n                  <jats:p>In this tutorial, we first highlight the importance of DSD in various applications and the unique challenges that need to be addressed. Subsequently, we classify existing DSD solutions into several groups, which cover around 50 research papers published in many well-known venues (e.g., SIGMOD, PVLDB, TODS, WWW), and conduct a thorough review of these solutions in each group. Afterwards, we analyze and compare the models and solutions in these works. Finally, we point out a list of promising future research directions. We believe that this tutorial not only helps researchers have a better understanding of existing densest subgraph models and solutions, but also provides them insights for future study.<\/jats:p>","DOI":"10.14778\/3554821.3554895","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T18:28:39Z","timestamp":1664476119000},"page":"3766-3769","source":"Crossref","is-referenced-by-count":23,"title":["Densest subgraph discovery on large graphs"],"prefix":"10.14778","volume":"15","author":[{"given":"Yixiang","family":"Fang","sequence":"first","affiliation":[{"name":"The Chinese University of Hong, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wensheng","family":"Luo","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenhao","family":"Ma","sequence":"additional","affiliation":[{"name":"The University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1824777.1824780"},{"key":"e_1_2_1_2_1","volume-title":"Finding dense subgraphs with size bounds","author":"Andersen Reid","unstructured":"Reid Andersen and Kumar Chellapilla . 2009. Finding dense subgraphs with size bounds . In WAW. Springer , 25--37. Reid Andersen and Kumar Chellapilla. 2009. Finding dense subgraphs with size bounds. In WAW. Springer, 25--37."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00778-013-0340-z"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1999.1062"},{"key":"e_1_2_1_5_1","volume-title":"Densest Subgraph in Streaming and MapReduce. PVLDB 5, 5","author":"Bahmani Bahman","year":"2012","unstructured":"Bahman Bahmani , Ravi Kumar , and Sergei Vassilvitskii . 2012. Densest Subgraph in Streaming and MapReduce. PVLDB 5, 5 ( 2012 ). Bahman Bahmani, Ravi Kumar, and Sergei Vassilvitskii. 2012. Densest Subgraph in Streaming and MapReduce. PVLDB 5, 5 (2012)."},{"key":"e_1_2_1_6_1","volume-title":"Francesco Gullo, and Mauro Sozio.","author":"Balalau Oana Denisa","year":"2015","unstructured":"Oana Denisa Balalau , Francesco Bonchi , TH Hubert Chan , Francesco Gullo, and Mauro Sozio. 2015 . Finding subgraphs with maximum total density and limited overlap. In WSDM. 379--388. Oana Denisa Balalau, Francesco Bonchi, TH Hubert Chan, Francesco Gullo, and Mauro Sozio. 2015. Finding subgraphs with maximum total density and limited overlap. In WSDM. 379--388."},{"key":"e_1_2_1_7_1","volume-title":"Polynomial integrality gaps for strong sdp relaxations of densest k-subgraph","author":"Bhaskara Aditya","unstructured":"Aditya Bhaskara , Moses Charikar , Venkatesan Guruswami , Aravindan Vijayaraghavan , and Yuan Zhou . 2012. Polynomial integrality gaps for strong sdp relaxations of densest k-subgraph . In SODA. SIAM , 388--405. Aditya Bhaskara, Moses Charikar, Venkatesan Guruswami, Aravindan Vijayaraghavan, and Yuan Zhou. 2012. Polynomial integrality gaps for strong sdp relaxations of densest k-subgraph. In SODA. SIAM, 388--405."},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","unstructured":"Sayan Bhattacharya Monika Henzinger Danupon Nanongkai and Charalampos Tsourakakis. 2015. Space-and time-efficient algorithm for maintaining dense subgraphs on one-pass dynamic streams. In STOC. 173--182.  Sayan Bhattacharya Monika Henzinger Danupon Nanongkai and Charalampos Tsourakakis. 2015. Space-and time-efficient algorithm for maintaining dense subgraphs on one-pass dynamic streams. In STOC. 173--182.","DOI":"10.1145\/2746539.2746592"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2021.08.032"},{"key":"e_1_2_1_10_1","volume-title":"Flowless: Extracting densest subgraphs without flow computations. In WWW.","author":"Boob Digvijay","year":"2020","unstructured":"Digvijay Boob , Yu Gao , Richard Peng , Saurabh Sawlani , Charalampos Tsourakakis , Di Wang , and Junxing Wang . 2020 . Flowless: Extracting densest subgraphs without flow computations. In WWW. Digvijay Boob, Yu Gao, Richard Peng, Saurabh Sawlani, Charalampos Tsourakakis, Di Wang, and Junxing Wang. 2020. Flowless: Extracting densest subgraphs without flow computations. In WWW."},{"key":"e_1_2_1_11_1","volume-title":"Exact and approximation algorithms for densest k-subgraph","author":"Bourgeois Nicolas","unstructured":"Nicolas Bourgeois , Aristotelis Giannakos , Giorgio Lucarelli , Ioannis Milis , and Vangelis Th Paschos . 2013. Exact and approximation algorithms for densest k-subgraph . In WALCOM. Springer , 114--125. Nicolas Bourgeois, Aristotelis Giannakos, Giorgio Lucarelli, Ioannis Milis, and Vangelis Th Paschos. 2013. Exact and approximation algorithms for densest k-subgraph. In WALCOM. Springer, 114--125."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1341531.1341547"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41965-019-00030-1"},{"key":"e_1_2_1_14_1","doi-asserted-by":"crossref","unstructured":"Lijun Chang and Miao Qiao. 2020. Deconstruct Densest Subgraphs. In WWW. 2747--2753.  Lijun Chang and Miao Qiao. 2020. Deconstruct Densest Subgraphs. 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