{"paper":{"title":"Permutation Reconstruction from Differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marzio De Biasi","submitted_at":"2014-10-23T15:28:42Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6396","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}