{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/practical-parallel-algorithms-for-near","title":"Practical Parallel Algorithms for Near-Optimal Densest Subgraphs on Massive Graphs","arxiv_id":"2311.04333","date":"2023-11-07","proceeding":null,"authors":["Pattara Sukprasert","Quanquan C. Liu","Laxman Dhulipala","Julian Shun"],"abstract":"The densest subgraph problem has received significant attention, both in theory and in practice, due to its applications in problems such as community detection, social network analysis, and spam detection. Due to the high cost of obtaining exact solutions, much attention has focused on designing approximate densest subgraph algorithms. However, existing approaches are not able to scale to massive graphs with billions of edges. In this paper, we introduce a new framework that combines approximate densest subgraph algorithms with a pruning optimization. We design new parallel variants of the state-of-the-art sequential Greedy++ algorithm, and plug it into our framework in conjunction with a parallel pruning technique based on $k$-core decomposition to obtain parallel $(1+\\varepsilon)$-approximate densest subgraph algorithms. On a single thread, our algorithms achieve $2.6$--$34\\times$ speedup over Greedy++, and obtain up to $22.37\\times$ self relative parallel speedup on a 30-core machine with two-way hyper-threading. Compared with the state-of-the-art parallel algorithm by Harb et al. [NeurIPS'22], we achieve up to a $114\\times$ speedup on the same machine. Finally, against the recent sequential algorithm of Xu et al. [PACMMOD'23], we achieve up to a $25.9\\times$ speedup. The scalability of our algorithms enables us to obtain near-optimal density statistics on the hyperlink2012 (with roughly 113 billion edges) and clueweb (with roughly 37 billion edges) graphs for the first time in the literature.","url_abs":"https://arxiv.org/abs/2311.04333v1","url_pdf":"https://arxiv.org/pdf/2311.04333v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"practical-parallel-algorithms-for-near","repo_url":"https://github.com/pattaras/gbbs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2311.04333","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2311.04333"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/pattaras/gbbs","reach":null}],"summary":{"ran":1,"unverified":4},"by_repo_kind":{"official":{"samples":5,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"5cc5de2d41565d8e","entry":"shellGetOutput","repo":"pattaras/gbbs","repo_kind":"official","path":"benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","file_url":"https://github.com/pattaras/gbbs/blob/HEAD/benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5cc5de2d41565d8e"}},{"code_sha256_prefix":"577457c09fe347b1","entry":"Alarm","repo":"pattaras/gbbs","repo_kind":"official","path":"benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","file_url":"https://github.com/pattaras/gbbs/blob/HEAD/benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"577457c09fe347b1"}},{"code_sha256_prefix":"98eb12713087c3c6","entry":"alarm_handler","repo":"pattaras/gbbs","repo_kind":"official","path":"benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","file_url":"https://github.com/pattaras/gbbs/blob/HEAD/benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"98eb12713087c3c6"}},{"code_sha256_prefix":"ec908f5fec4c0ce6","entry":"appendToFile","repo":"pattaras/gbbs","repo_kind":"official","path":"benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","file_url":"https://github.com/pattaras/gbbs/blob/HEAD/benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ec908f5fec4c0ce6"}},{"code_sha256_prefix":"085d8727fb8b27ee","entry":"main","repo":"pattaras/gbbs","repo_kind":"official","path":"benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","file_url":"https://github.com/pattaras/gbbs/blob/HEAD/benchmarks/ApproximateDensestSubgraph/GreedyPlusPlus/run_experiment.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"085d8727fb8b27ee"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}