{"paper":{"title":"A faster algorithm for the discrete Fr\\'echet distance under translation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Haim Kaplan, Micha Sharir, Rinat Ben Avraham","submitted_at":"2015-01-15T16:00:50Z","abstract_excerpt":"The discrete Fr\\'echet distance is a useful similarity measure for comparing two sequences of points $P=(p_1,\\ldots, p_m)$ and $Q=(q_1,\\ldots,q_n)$. In many applications, the quality of the matching can be improved if we let $Q$ undergo some transformation relative to $P$. In this paper we consider the problem of finding a translation of $Q$ that brings the discrete Fr\\'echet distance between $P$ and $Q$ to a minimum. We devise an algorithm that computes the minimum discrete Fr\\'echet distance under translation in $\\mathbb{R}^2$, and runs in $O(m^3n^2(1+\\log(n/m))\\log(m+n))$ time, assuming $m\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03724","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"}