{"paper":{"title":"A faster algorithm for the Fr\\'echet distance in 1D for the imbalanced case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anne Driemel, Lotte Blank","submitted_at":"2024-04-29T14:37:56Z","abstract_excerpt":"The fine-grained complexity of computing the Fr\\'echet distance has been a topic of much recent work, starting with the quadratic SETH-based conditional lower bound by Bringmann from 2014. Subsequent work established largely the same complexity lower bounds for the Fr\\'echet distance in 1D. However, the imbalanced case, which was shown by Bringmann to be tight in dimensions $d\\geq 2$, was still left open. Filling in this gap, we show that a faster algorithm for the Fr\\'echet distance in the imbalanced case is possible: Given two 1-dimensional curves of complexity $n$ and $n^{\\alpha}$ for some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18738","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.18738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}