{"paper":{"title":"Clustering time series under the Fr\\'echet distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Amer Krivo\\v{s}ija, Anne Driemel, Christian Sohler","submitted_at":"2015-12-14T14:56:37Z","abstract_excerpt":"The Fr\\'echet distance is a popular distance measure for curves. We study the problem of clustering time series under the Fr\\'echet distance. In particular, we give $(1+\\varepsilon)$-approximation algorithms for variations of the following problem with parameters $k$ and $\\ell$. Given $n$ univariate time series $P$, each of complexity at most $m$, we find $k$ time series, not necessarily from $P$, which we call \\emph{cluster centers} and which each have complexity at most $\\ell$, such that (a) the maximum distance of an element of $P$ to its nearest cluster center or (b) the sum of these dista"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04349","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"}