{"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/correlation-clustering-algorithm-for-dynamic","title":"Correlation Clustering Algorithm for Dynamic Complete Signed Graphs: An Index-based Approach","arxiv_id":"2301.00384","date":"2023-01-01","proceeding":null,"authors":["Ali Shakiba"],"abstract":"In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\\times\\left( 2+ \\alpha (G) \\right)+n)$ to $O(m+n)$ for any given value of $\\varepsilon$ for a complete signed graph with $n$ vertices and $m$ positive edges where $\\alpha(G)$ is the arboricity of the graph. Our approach gives the same output as the original algorithm and makes it possible to implement the algorithm in a full dynamic setting where edge sign flipping and vertex addition/removal are allowed. Constructing this index costs $O(m)$ memory and $O(m\\times\\alpha(G))$ time. We also studied the structural properties of the non-agreement measure used in the approximation algorithm. The theoretical results are accompanied by a full set of experiments concerning seven real-world graphs. These results shows superiority of our index-based algorithm to the non-index one by a decrease of %34 in time on average.","url_abs":"https://arxiv.org/abs/2301.00384v1","url_pdf":"https://arxiv.org/pdf/2301.00384v1.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":"abstracts"},"code_links":[{"paper_slug":"correlation-clustering-algorithm-for-dynamic","repo_url":"https://github.com/alishakiba/correlation-clustering-algorithm-for-dynamic-complete-signed-graphs-an-index-based-approach","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.00384","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}