{"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/permutation-reconstruction-from-differences","title":"Permutation Reconstruction from Differences","arxiv_id":"1410.6396","date":"2014-10-23","proceeding":null,"authors":["Marzio De Biasi"],"abstract":"We prove that the problem of reconstructing a permutation $\\pi_1,\\dotsc,\\pi_n$ of the integers $[1\\dotso n]$ given the absolute differences $|\\pi_{i+1}-\\pi_i|$, $i = 1,\\dotsc,n-1$ is NP-complete. As an intermediate step we first prove the NP-completeness of the decision version of a new puzzle game that we call Crazy Frog Puzzle. The permutation reconstruction from differences is one of the simplest combinatorial problems that have been proved to be computationally intractable.","url_abs":"http://arxiv.org/abs/1410.6396v2","url_pdf":"http://arxiv.org/pdf/1410.6396v2.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":"permutation-reconstruction-from-differences","repo_url":"https://github.com/maxtuno/PEQNP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"permutation-reconstruction-from-differences","repo_url":"https://github.com/maxtuno/Permutation-Reconstruction-from-Differences","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}