{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UAXRNH3NNLSD5EK5AR5P4HSYKM","short_pith_number":"pith:UAXRNH3N","schema_version":"1.0","canonical_sha256":"a02f169f6d6ae43e915d047afe1e58531f76e69c9611ff9845e6fc9a63bdda5e","source":{"kind":"arxiv","id":"1509.07214","version":1},"attestation_state":"computed","paper":{"title":"Computing the Geodesic Centers of a Polygonal Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Matias Korman, Sang Won Bae, Yoshio Okamoto","submitted_at":"2015-09-24T02:47:42Z","abstract_excerpt":"We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is $O(n^{12+\\epsilon})$ for any $\\epsilon>0$, where $n$ is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an $O(n \\log n)$-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes."},"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":"1509.07214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-24T02:47:42Z","cross_cats_sorted":[],"title_canon_sha256":"9fcaf928a154a3e0ca1e0f0023fec72f63d32cd2034197e9dd83f30f915ab3b0","abstract_canon_sha256":"1dd3359d1c13f299ece4a181c9e379c5fdc024410e183c89251f6cbf5427c5ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:09.547522Z","signature_b64":"4IAPRj0Z1lo83mQPKel+yl6NdG55VXV6spqvFbuf2ZFDPoPUQSC5Yye01svjPkNKGGz75bYP8hkfcybpXu6gDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a02f169f6d6ae43e915d047afe1e58531f76e69c9611ff9845e6fc9a63bdda5e","last_reissued_at":"2026-05-18T01:32:09.546816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:09.546816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the Geodesic Centers of a Polygonal Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Matias Korman, Sang Won Bae, Yoshio Okamoto","submitted_at":"2015-09-24T02:47:42Z","abstract_excerpt":"We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is $O(n^{12+\\epsilon})$ for any $\\epsilon>0$, where $n$ is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an $O(n \\log n)$-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07214","kind":"arxiv","version":1},"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":"1509.07214","created_at":"2026-05-18T01:32:09.546924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07214v1","created_at":"2026-05-18T01:32:09.546924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07214","created_at":"2026-05-18T01:32:09.546924+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAXRNH3NNLSD","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAXRNH3NNLSD5EK5","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAXRNH3N","created_at":"2026-05-18T12:29:44.643036+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/UAXRNH3NNLSD5EK5AR5P4HSYKM","json":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM.json","graph_json":"https://pith.science/api/pith-number/UAXRNH3NNLSD5EK5AR5P4HSYKM/graph.json","events_json":"https://pith.science/api/pith-number/UAXRNH3NNLSD5EK5AR5P4HSYKM/events.json","paper":"https://pith.science/paper/UAXRNH3N"},"agent_actions":{"view_html":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM","download_json":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM.json","view_paper":"https://pith.science/paper/UAXRNH3N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07214&json=true","fetch_graph":"https://pith.science/api/pith-number/UAXRNH3NNLSD5EK5AR5P4HSYKM/graph.json","fetch_events":"https://pith.science/api/pith-number/UAXRNH3NNLSD5EK5AR5P4HSYKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM/action/storage_attestation","attest_author":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM/action/author_attestation","sign_citation":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM/action/citation_signature","submit_replication":"https://pith.science/pith/UAXRNH3NNLSD5EK5AR5P4HSYKM/action/replication_record"}},"created_at":"2026-05-18T01:32:09.546924+00:00","updated_at":"2026-05-18T01:32:09.546924+00:00"}