{"paper":{"title":"Improved Bounds for Testing Forbidden Order Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"Cl\\'ement L. Canonne, Omri Ben-Eliezer","submitted_at":"2017-10-29T18:06:27Z","abstract_excerpt":"A sequence $f\\colon\\{1,\\dots,n\\}\\to\\mathbb{R}$ contains a permutation $\\pi$ of length $k$ if there exist $i_1<\\dots<i_k$ such that, for all $x,y$, $f(i_x)<f(i_y)$ if and only if $\\pi(x)<\\pi(y)$; otherwise, $f$ is said to be $\\pi$-free. In this work, we consider the problem of testing for $\\pi$-freeness with one-sided error, continuing the investigation of [Newman et al., SODA'17].\n  We demonstrate a surprising behavior for non-adaptive tests with one-sided error: While a trivial sampling-based approach yields an $\\varepsilon$-test for $\\pi$-freeness making $\\Theta(\\varepsilon^{-1/k} n^{1-1/k})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10660","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"}