{"paper":{"title":"Approximating $(k,\\ell)$-center clustering for curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IR"],"primary_cat":"cs.CG","authors_text":"Anne Driemel, Irina Kostitsyna, Joachim Gudmundsson, Kevin Buchin, Maarten L\\\"offler, Martijn Struijs, Michael Horton","submitted_at":"2018-05-03T21:32:41Z","abstract_excerpt":"The Euclidean $k$-center problem is a classical problem that has been extensively studied in computer science. Given a set $\\mathcal{G}$ of $n$ points in Euclidean space, the problem is to determine a set $\\mathcal{C}$ of $k$ centers (not necessarily part of $\\mathcal{G}$) such that the maximum distance between a point in $\\mathcal{G}$ and its nearest neighbor in $\\mathcal{C}$ is minimized. In this paper we study the corresponding $(k,\\ell)$-center problem for polygonal curves under the Fr\\'echet distance, that is, given a set $\\mathcal{G}$ of $n$ polygonal curves in $\\mathbb{R}^d$, each of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01547","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"}