{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AV7ERSCWX3WPDK3TQA5624XVI7","short_pith_number":"pith:AV7ERSCW","schema_version":"1.0","canonical_sha256":"057e48c856beecf1ab73803bed72f547d5d4cb887fbde8577ea97794a34301e6","source":{"kind":"arxiv","id":"1605.03692","version":2},"attestation_state":"computed","paper":{"title":"The Non-Uniform k-Center Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Deeparnab Chakrabarty, Prachi Goyal, Ravishankar Krishnaswamy","submitted_at":"2016-05-12T06:18:32Z","abstract_excerpt":"In this paper, we introduce and study the Non-Uniform k-Center problem (NUkC). Given a finite metric space $(X,d)$ and a collection of balls of radii $\\{r_1\\geq \\cdots \\ge r_k\\}$, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation $\\alpha$, such that the union of balls of radius $\\alpha\\cdot r_i$ around the $i$th center covers all the points in $X$. This problem naturally arises as a min-max vehicle routing problem with fleets of different speeds.\n  The NUkC problem generalizes the classic $k$-center problem when all the $k$ radii are the"},"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":"1605.03692","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-12T06:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"de1df50ef8396d8a455d442b133daefff0a8a5908fea7220039873d8ef0ee2ae","abstract_canon_sha256":"ff01f0efd2b7eb1e350efe41ab65ffdeaec18f85641e0fe34ca280bcc691639d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:54.628660Z","signature_b64":"IOm5y7SUDPpba5HZ0UquGmeTWAcsRrnAQIK5qX96ifI7I/9UgDQ0skeoJ8opsakCVABPqtTMMrONuPpvFvcIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"057e48c856beecf1ab73803bed72f547d5d4cb887fbde8577ea97794a34301e6","last_reissued_at":"2026-05-18T01:14:54.628143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:54.628143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Non-Uniform k-Center Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Deeparnab Chakrabarty, Prachi Goyal, Ravishankar Krishnaswamy","submitted_at":"2016-05-12T06:18:32Z","abstract_excerpt":"In this paper, we introduce and study the Non-Uniform k-Center problem (NUkC). Given a finite metric space $(X,d)$ and a collection of balls of radii $\\{r_1\\geq \\cdots \\ge r_k\\}$, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation $\\alpha$, such that the union of balls of radius $\\alpha\\cdot r_i$ around the $i$th center covers all the points in $X$. This problem naturally arises as a min-max vehicle routing problem with fleets of different speeds.\n  The NUkC problem generalizes the classic $k$-center problem when all the $k$ radii are the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03692","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":"1605.03692","created_at":"2026-05-18T01:14:54.628218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03692v2","created_at":"2026-05-18T01:14:54.628218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03692","created_at":"2026-05-18T01:14:54.628218+00:00"},{"alias_kind":"pith_short_12","alias_value":"AV7ERSCWX3WP","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AV7ERSCWX3WPDK3T","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AV7ERSCW","created_at":"2026-05-18T12:30:07.202191+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/AV7ERSCWX3WPDK3TQA5624XVI7","json":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7.json","graph_json":"https://pith.science/api/pith-number/AV7ERSCWX3WPDK3TQA5624XVI7/graph.json","events_json":"https://pith.science/api/pith-number/AV7ERSCWX3WPDK3TQA5624XVI7/events.json","paper":"https://pith.science/paper/AV7ERSCW"},"agent_actions":{"view_html":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7","download_json":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7.json","view_paper":"https://pith.science/paper/AV7ERSCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03692&json=true","fetch_graph":"https://pith.science/api/pith-number/AV7ERSCWX3WPDK3TQA5624XVI7/graph.json","fetch_events":"https://pith.science/api/pith-number/AV7ERSCWX3WPDK3TQA5624XVI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7/action/storage_attestation","attest_author":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7/action/author_attestation","sign_citation":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7/action/citation_signature","submit_replication":"https://pith.science/pith/AV7ERSCWX3WPDK3TQA5624XVI7/action/replication_record"}},"created_at":"2026-05-18T01:14:54.628218+00:00","updated_at":"2026-05-18T01:14:54.628218+00:00"}