{"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/fast-and-compact-planar-embeddings","title":"Fast and Compact Planar Embeddings","arxiv_id":"1610.00130","date":"2016-10-01","proceeding":null,"authors":["Leo Ferres","José Fuentes","Travis Gagie","Meng He","Gonzalo Navarro"],"abstract":"There are many representations of planar graphs, but few are as elegant as Tur\\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main disadvantage has been that \"it does not allow efficient searching\" (Jacobson, 1989). In this paper we show how to add a sublinear number of bits to Tur\\'an's representation such that it supports fast navigation while retaining simplicity. As a consequence of the inherited simplicity, we offer the first efficient parallel construction of a compact encoding of a planar graph embedding. Our experimental results show that the resulting representation uses about 6 bits per edge in practice, supports basic navigation operations within a few microseconds, and can be built sequentially at a rate below 1 microsecond per edge, featuring a linear speedup with a parallel efficiency around 50\\% for large datasets.","url_abs":"http://arxiv.org/abs/1610.00130v7","url_pdf":"http://arxiv.org/pdf/1610.00130v7.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":"fast-and-compact-planar-embeddings","repo_url":"https://github.com/jfuentess/sdsl-lite","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}