{"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/cardinality-constrained-submodular","title":"Cardinality constrained submodular maximization for random streams","arxiv_id":"2111.07217","date":"2021-11-14","proceeding":null,"authors":["Paul Liu","Aviad Rubinstein","Jan Vondrak","Junyao Zhao"],"abstract":"We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a single-pass $(1-1/e-\\varepsilon)$-approximation algorithm using only linear memory, but their exponential dependence on $\\varepsilon$ makes it impractical even for $\\varepsilon=0.1$. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the $\\varepsilon$-dependence (in particular, $O(k/\\varepsilon)$ memory). Extending these techniques, we also give a simple $(1/e-\\varepsilon)$-approximation for non-monotone functions in $O(k/\\varepsilon)$ memory. For the monotone case, we also give a corresponding unconditional hardness barrier of $1-1/e+\\varepsilon$ for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.","url_abs":"https://arxiv.org/abs/2111.07217v1","url_pdf":"https://arxiv.org/pdf/2111.07217v1.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":"cardinality-constrained-submodular","repo_url":"https://github.com/where-is-paul/submodular-streaming","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2111.07217","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}