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VLDB Endow."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>\n            Densest subgraph search, aiming to identify a subgraph with maximum edge density, faces limitations as the edge density inadequately reflects biases towards a given vertex set\n            <jats:italic>R.<\/jats:italic>\n            To address this, the\n            <jats:italic>R<\/jats:italic>\n            -subgraph density was introduced, refining the doubled edge density by penalizing vertices in a subgraph but not in\n            <jats:italic>R<\/jats:italic>\n            , using the degree as a penalty factor. This advancement leads to the Anchored Densest Subgraph (ADS) search problem, which finds the subgraph \u0160 with the highest\n            <jats:italic>R<\/jats:italic>\n            -subgraph density for a given set\n            <jats:italic>R.<\/jats:italic>\n            Nonetheless, current algorithms for ADS search face significant inefficiencies in handling large-scale graphs or the sizable\n            <jats:italic>R<\/jats:italic>\n            set. Furthermore, these algorithms require re-computing the ADS whenever the graph is updated, complicating the efficient maintenance within dynamic graphs. To tackle these challenges, we propose the concept of integer\n            <jats:italic>R<\/jats:italic>\n            -subgraph density and study the problem of finding a subgraph\n            <jats:italic>S<\/jats:italic>\n            * \u2286\n            <jats:italic>V<\/jats:italic>\n            with the highest integer\n            <jats:italic>R<\/jats:italic>\n            -subgraph density. We reveal that the\n            <jats:italic>R<\/jats:italic>\n            -subgraph density of\n            <jats:italic>S*<\/jats:italic>\n            provides an additive approximation to that of ADS with a difference of less than 1, and hence\n            <jats:italic>S<\/jats:italic>\n            * is termed the Approximate Anchored Densest Subgraph (AADS). For searching the AADS, we present an efficient global algorithm incorporating the re-orientation network flow technique and binary search, operating in a time polynomial to the graph's size. Additionally, we propose a novel local algorithm using shortest-path-based methods for the max-flow computation from\n            <jats:italic>s<\/jats:italic>\n            to\n            <jats:italic>t<\/jats:italic>\n            around\n            <jats:italic>R<\/jats:italic>\n            , markedly boosting performance in scenarios with larger\n            <jats:italic>R<\/jats:italic>\n            sets. For dynamic graphs, both basic and improved algorithms are developed to efficiently maintain the AADS when an edge is updated. Extensive experiments and a case study demonstrate the efficiency, scalability, and effectiveness of our solutions.\n          <\/jats:p>","DOI":"10.14778\/3712221.3712230","type":"journal-article","created":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T18:03:04Z","timestamp":1744048984000},"page":"623-636","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximate Anchored Densest Subgraph Search on Large Static and Dynamic Graphs"],"prefix":"10.14778","volume":"18","author":[{"given":"Qi","family":"Zhang","sequence":"first","affiliation":[{"name":"University of Science and Technology Beijing, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yalong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rong-Hua","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoren","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,4,7]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Fabeah AduOppong Casey K Gardiner Apu Kapadia and Patrick P Tsang. 2008. 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