{"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/engineering-data-reduction-for-nested","title":"Engineering Data Reduction for Nested Dissection","arxiv_id":"2004.11315","date":"2020-04-23","proceeding":null,"authors":["Lara Ost","Christian Schulz","Darren Strash"],"abstract":"Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the so-called fill-in. In this paper, we engineer new data reduction rules for the minimum fill-in problem, which significantly reduce the size of the graph while producing an equivalent (or near-equivalent) instance. By applying both new and existing data reduction rules exhaustively before nested dissection, we obtain improved quality and at the same time large improvements in running time on a variety of instances. Our overall algorithm outperforms the state-of-the-art significantly: it not only yields better elimination orders, but it does so significantly faster than previously possible. For example, on road networks, where nested dissection algorithms are typically used as a preprocessing step for shortest path computations, our algorithms are on average six times faster than Metis while computing orderings with less fill-in.","url_abs":"https://arxiv.org/abs/2004.11315v1","url_pdf":"https://arxiv.org/pdf/2004.11315v1.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":"engineering-data-reduction-for-nested","repo_url":"https://github.com/KaHIP/KaHIP","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"engineering-data-reduction-for-nested","repo_url":"https://github.com/hu-macsy/KaHIP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"engineering-data-reduction-for-nested","repo_url":"https://github.com/schulzchristian/KaHIP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}