{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PDPBZLCHATNND5LJKBN5EIMTIH","short_pith_number":"pith:PDPBZLCH","schema_version":"1.0","canonical_sha256":"78de1cac4704dad1f569505bd2219341c85b8877a675205635ef03e42e37843c","source":{"kind":"arxiv","id":"1301.3471","version":2},"attestation_state":"computed","paper":{"title":"Embedding a balanced binary tree on a bounded point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Alireza Bagheri, Fatemeh Rajabi-Alni","submitted_at":"2013-01-15T20:06:36Z","abstract_excerpt":"Given an undirected planar graph G with n vertices and a set S of n points inside a simple polygon P, a point-set embedding of G on S is a planar drawing of G such that each vertex is mapped to a distinct point of S and the edges are polygonal chains surrounded by P. A special case of the embedding problem is that in which G is a balanced binary tree. In this paper, we present a new algorithm for embedding an n-vertex balanced binary tree BBT on a set S of n points bounded by a simple m-gon P in O(m^2 + n(log n)^2 + mn) time with at most O(m) bends per edge."},"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":"1301.3471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-15T20:06:36Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8bc106e448fbb54eda3bf7e33f83464560e8edd60f2c12f73e2b69a6ef1174fa","abstract_canon_sha256":"3ee0808da5d221b97d884d3e79b481ee162bca7b64176f0762d010d25a87168d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:50.245746Z","signature_b64":"Fhn5FBw71ErRyY4nW2pNPDqYWC7q4vLv3RwGRzltSFGAzuii8BjeDV2yXniydMVOK/l2T9nb+L3wlyllg3ZPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78de1cac4704dad1f569505bd2219341c85b8877a675205635ef03e42e37843c","last_reissued_at":"2026-05-18T03:09:50.244775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:50.244775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding a balanced binary tree on a bounded point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Alireza Bagheri, Fatemeh Rajabi-Alni","submitted_at":"2013-01-15T20:06:36Z","abstract_excerpt":"Given an undirected planar graph G with n vertices and a set S of n points inside a simple polygon P, a point-set embedding of G on S is a planar drawing of G such that each vertex is mapped to a distinct point of S and the edges are polygonal chains surrounded by P. A special case of the embedding problem is that in which G is a balanced binary tree. In this paper, we present a new algorithm for embedding an n-vertex balanced binary tree BBT on a set S of n points bounded by a simple m-gon P in O(m^2 + n(log n)^2 + mn) time with at most O(m) bends per edge."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3471","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":"1301.3471","created_at":"2026-05-18T03:09:50.244935+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3471v2","created_at":"2026-05-18T03:09:50.244935+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3471","created_at":"2026-05-18T03:09:50.244935+00:00"},{"alias_kind":"pith_short_12","alias_value":"PDPBZLCHATNN","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PDPBZLCHATNND5LJ","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PDPBZLCH","created_at":"2026-05-18T12:27:54.935989+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/PDPBZLCHATNND5LJKBN5EIMTIH","json":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH.json","graph_json":"https://pith.science/api/pith-number/PDPBZLCHATNND5LJKBN5EIMTIH/graph.json","events_json":"https://pith.science/api/pith-number/PDPBZLCHATNND5LJKBN5EIMTIH/events.json","paper":"https://pith.science/paper/PDPBZLCH"},"agent_actions":{"view_html":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH","download_json":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH.json","view_paper":"https://pith.science/paper/PDPBZLCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3471&json=true","fetch_graph":"https://pith.science/api/pith-number/PDPBZLCHATNND5LJKBN5EIMTIH/graph.json","fetch_events":"https://pith.science/api/pith-number/PDPBZLCHATNND5LJKBN5EIMTIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH/action/storage_attestation","attest_author":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH/action/author_attestation","sign_citation":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH/action/citation_signature","submit_replication":"https://pith.science/pith/PDPBZLCHATNND5LJKBN5EIMTIH/action/replication_record"}},"created_at":"2026-05-18T03:09:50.244935+00:00","updated_at":"2026-05-18T03:09:50.244935+00:00"}