{"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/12120884","title":"Maximizing Social Influence in Nearly Optimal Time","arxiv_id":"1212.0884","date":"2012-12-04","proceeding":null,"authors":["Christian Borgs","Michael Brautbar","Jennifer Chayes","Brendan Lucier"],"abstract":"Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network diffusion. Runtime is a primary consideration for this problem due to the massive size of the relevant input networks. We provide a fast algorithm for the influence maximization problem, obtaining the near-optimal approximation factor of (1 - 1/e - epsilon), for any epsilon > 0, in time O((m+n)k log(n) / epsilon^2). Our algorithm is runtime-optimal (up to a logarithmic factor) and substantially improves upon the previously best-known algorithms which run in time Omega(mnk POLY(1/epsilon)). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O(beta(m+n)k log(n)) steps for some beta < 1 (which can depend on n), then it returns a solution with approximation factor O(beta). Finally, we show that this runtime is optimal (up to logarithmic factors) for any beta and fixed seed size k.","url_abs":"http://arxiv.org/abs/1212.0884v5","url_pdf":"http://arxiv.org/pdf/1212.0884v5.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":"12120884","repo_url":"https://github.com/MehmetBarutcu/Streaming-Algorithm-for-Monotone-k-Submodular-Maximization-with-Cardinality-Constraints","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1212.0884","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}