{"paper":{"title":"On testing substitutability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"cs.DS","authors_text":"Cosmina Croitoru, Kurt Mehlhorn","submitted_at":"2018-05-19T19:09:27Z","abstract_excerpt":"The papers~\\cite{hatfimmokomi11} and~\\cite{azizbrilharr13} propose algorithms for testing whether the choice function induced by a (strict) preference list of length $N$ over a universe $U$ is substitutable. The running time of these algorithms is $O(|U|^3\\cdot N^3)$, respectively $O(|U|^2\\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07642","kind":"arxiv","version":1},"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"}