{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FA5HXE7HH475ZEKD4W6GH3OPWB","short_pith_number":"pith:FA5HXE7H","schema_version":"1.0","canonical_sha256":"283a7b93e73f3fdc9143e5bc63edcfb0525f4fe8301c3402c180be5f831dae75","source":{"kind":"arxiv","id":"1502.04918","version":3},"attestation_state":"computed","paper":{"title":"A PTAS for the Weighted Unit Disk Cover Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jian Li, Yifei Jin","submitted_at":"2015-02-17T15:18:40Z","abstract_excerpt":"We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (\\UDC) problem asks for a subset of disks of minimum total weight that covers all given points. \\UDC\\ is one of the geometric set cover problems, which have been studied extensively for the past two decades (for many different geometric range spaces, such as (unit) disks, halfspaces, rectangles, triangles). It is known that the unweighted \\UDC\\ problem is NP-hard and admits a polynomial-time approximation scheme (PTAS). For the weighted \\UDC\\ problem, several constant approximat"},"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":"1502.04918","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-02-17T15:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"07589013d7f207838c6d59e3425c2693b44a3135fb3653a09ba8cafaa98a003a","abstract_canon_sha256":"7491cfce47cc2977643aca547cb76568a611f2cd28afef46e9efb0cec8d2bc6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:04.235733Z","signature_b64":"qOBbQ5S3VhYCA899pdt66rvgVIrCFmQ+17VzIWfeDxwl86XCqZwkH8pW8yXN69p+WOGF1bqFsvnoMcFZiFqnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"283a7b93e73f3fdc9143e5bc63edcfb0525f4fe8301c3402c180be5f831dae75","last_reissued_at":"2026-05-18T01:23:04.235159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:04.235159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A PTAS for the Weighted Unit Disk Cover Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jian Li, Yifei Jin","submitted_at":"2015-02-17T15:18:40Z","abstract_excerpt":"We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (\\UDC) problem asks for a subset of disks of minimum total weight that covers all given points. \\UDC\\ is one of the geometric set cover problems, which have been studied extensively for the past two decades (for many different geometric range spaces, such as (unit) disks, halfspaces, rectangles, triangles). It is known that the unweighted \\UDC\\ problem is NP-hard and admits a polynomial-time approximation scheme (PTAS). For the weighted \\UDC\\ problem, several constant approximat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04918","kind":"arxiv","version":3},"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":"1502.04918","created_at":"2026-05-18T01:23:04.235247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04918v3","created_at":"2026-05-18T01:23:04.235247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04918","created_at":"2026-05-18T01:23:04.235247+00:00"},{"alias_kind":"pith_short_12","alias_value":"FA5HXE7HH475","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FA5HXE7HH475ZEKD","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FA5HXE7H","created_at":"2026-05-18T12:29:19.899920+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/FA5HXE7HH475ZEKD4W6GH3OPWB","json":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB.json","graph_json":"https://pith.science/api/pith-number/FA5HXE7HH475ZEKD4W6GH3OPWB/graph.json","events_json":"https://pith.science/api/pith-number/FA5HXE7HH475ZEKD4W6GH3OPWB/events.json","paper":"https://pith.science/paper/FA5HXE7H"},"agent_actions":{"view_html":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB","download_json":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB.json","view_paper":"https://pith.science/paper/FA5HXE7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04918&json=true","fetch_graph":"https://pith.science/api/pith-number/FA5HXE7HH475ZEKD4W6GH3OPWB/graph.json","fetch_events":"https://pith.science/api/pith-number/FA5HXE7HH475ZEKD4W6GH3OPWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB/action/storage_attestation","attest_author":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB/action/author_attestation","sign_citation":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB/action/citation_signature","submit_replication":"https://pith.science/pith/FA5HXE7HH475ZEKD4W6GH3OPWB/action/replication_record"}},"created_at":"2026-05-18T01:23:04.235247+00:00","updated_at":"2026-05-18T01:23:04.235247+00:00"}