{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZPXWSIZT5VQ2IHDTK2OTK75BTF","short_pith_number":"pith:ZPXWSIZT","schema_version":"1.0","canonical_sha256":"cbef692333ed61a41c73569d357fa1994b2944ff5ae3b092ba9a5c8b81fc2ff4","source":{"kind":"arxiv","id":"1805.01547","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.01547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-05-03T21:32:41Z","cross_cats_sorted":["cs.IR"],"title_canon_sha256":"a4f10fdc8d646609c48765e0684ae8fcc70729e4b9541a9a2287331cdf34d3c1","abstract_canon_sha256":"873f4aee2eacdcd3fe81ce7b1d27f34da454eca06cb2d196b9ba94580bea4319"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:16.817402Z","signature_b64":"1FMQhB1a7N3dzz4sBEurhGM8iv3rqt0wtjSI4tMYIQudU1kLzyBpLJaC85f+boPGBbxYx2y7qcsYfgQs+6s2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbef692333ed61a41c73569d357fa1994b2944ff5ae3b092ba9a5c8b81fc2ff4","last_reissued_at":"2026-05-18T00:10:16.816932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:16.816932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.01547","created_at":"2026-05-18T00:10:16.817002+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01547v2","created_at":"2026-05-18T00:10:16.817002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01547","created_at":"2026-05-18T00:10:16.817002+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPXWSIZT5VQ2","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPXWSIZT5VQ2IHDT","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPXWSIZT","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF","json":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF.json","graph_json":"https://pith.science/api/pith-number/ZPXWSIZT5VQ2IHDTK2OTK75BTF/graph.json","events_json":"https://pith.science/api/pith-number/ZPXWSIZT5VQ2IHDTK2OTK75BTF/events.json","paper":"https://pith.science/paper/ZPXWSIZT"},"agent_actions":{"view_html":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF","download_json":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF.json","view_paper":"https://pith.science/paper/ZPXWSIZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01547&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPXWSIZT5VQ2IHDTK2OTK75BTF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPXWSIZT5VQ2IHDTK2OTK75BTF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF/action/storage_attestation","attest_author":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF/action/author_attestation","sign_citation":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF/action/citation_signature","submit_replication":"https://pith.science/pith/ZPXWSIZT5VQ2IHDTK2OTK75BTF/action/replication_record"}},"created_at":"2026-05-18T00:10:16.817002+00:00","updated_at":"2026-05-18T00:10:16.817002+00:00"}