{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6OF7WLIQIK736QF7DGCGHYKTFG","short_pith_number":"pith:6OF7WLIQ","schema_version":"1.0","canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","source":{"kind":"arxiv","id":"1607.02184","version":2},"attestation_state":"computed","paper":{"title":"Maximizing the Sum of Radii of Disjoint Balls or Disks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"David Eppstein","submitted_at":"2016-07-07T22:28:34Z","abstract_excerpt":"Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles (allowing 2-cycles) covering all vertices in a complete geometric graph. For points in a Euclidean space of any finite dimension~$d$, with any convex distance function on this space, this graph can be replaced by a sparse subgraph obeying a separator theorem. This graph structure leads to an algorithm for finding the optimum set of balls in time $O(n^{2-1/d})$,"},"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":"1607.02184","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"fc4e35fe4010abeaeacd63e3f6158c26ce6bd57305712409b9d6c2b5dbc01c47","abstract_canon_sha256":"f8ed3bb839fc3b63fa84f24933961c3785f90c8ee262853ec31869ab5424f483"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:37.001671Z","signature_b64":"P+fWRa2Mem1Rr2bRI7aoRt28KG47DIQX6zWrydP0R8nYM+elIMbYEUiLH7rbUiQrLa4Q/TDB1XncDuLt7h6jBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","last_reissued_at":"2026-05-18T00:33:37.001198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:37.001198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximizing the Sum of Radii of Disjoint Balls or Disks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"David Eppstein","submitted_at":"2016-07-07T22:28:34Z","abstract_excerpt":"Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles (allowing 2-cycles) covering all vertices in a complete geometric graph. For points in a Euclidean space of any finite dimension~$d$, with any convex distance function on this space, this graph can be replaced by a sparse subgraph obeying a separator theorem. This graph structure leads to an algorithm for finding the optimum set of balls in time $O(n^{2-1/d})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02184","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":"1607.02184","created_at":"2026-05-18T00:33:37.001262+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02184v2","created_at":"2026-05-18T00:33:37.001262+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02184","created_at":"2026-05-18T00:33:37.001262+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OF7WLIQIK73","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OF7WLIQIK736QF7","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OF7WLIQ","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13171","citing_title":"Parameterized Geometric Graph Modification with Disk Scaling","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG","json":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG.json","graph_json":"https://pith.science/api/pith-number/6OF7WLIQIK736QF7DGCGHYKTFG/graph.json","events_json":"https://pith.science/api/pith-number/6OF7WLIQIK736QF7DGCGHYKTFG/events.json","paper":"https://pith.science/paper/6OF7WLIQ"},"agent_actions":{"view_html":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG","download_json":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG.json","view_paper":"https://pith.science/paper/6OF7WLIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02184&json=true","fetch_graph":"https://pith.science/api/pith-number/6OF7WLIQIK736QF7DGCGHYKTFG/graph.json","fetch_events":"https://pith.science/api/pith-number/6OF7WLIQIK736QF7DGCGHYKTFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/action/storage_attestation","attest_author":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/action/author_attestation","sign_citation":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/action/citation_signature","submit_replication":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/action/replication_record"}},"created_at":"2026-05-18T00:33:37.001262+00:00","updated_at":"2026-05-18T00:33:37.001262+00:00"}