{"paper":{"title":"Single and multiple consecutive permutation motif search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adeline Pierrot, Djamal Belazzougui, Mathieu Raffinot, St\\'ephane Vialette","submitted_at":"2013-01-21T18:33:06Z","abstract_excerpt":"Let $t$ be a permutation (that shall play the role of the {\\em text}) on $[n]$ and a pattern $p$ be a sequence of $m$ distinct integer(s) of $[n]$, $m\\leq n$. The pattern $p$ occurs in $t$ in position $i$ if and only if $p_1... p_m$ is order-isomorphic to $t_i... t_{i+m-1}$, that is, for all $1 \\leq k< \\ell \\leq m$, $p_k>p_\\ell$ if and only if $t_{i+k-1}>t_{i+\\ell-1}$. Searching for a pattern $p$ in a text $t$ consists in identifying all occurrences of $p$ in $t$. We first present a forward automaton which allows us to search for $p$ in $t$ in $O(m^2\\log \\log m +n)$ time. We then introduce a M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4952","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"}