{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HCKFPCXRQPN7GY2A3YJVWTDWML","short_pith_number":"pith:HCKFPCXR","schema_version":"1.0","canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","source":{"kind":"arxiv","id":"1709.01456","version":1},"attestation_state":"computed","paper":{"title":"Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Kshitij Jain, Martin Derka, Therese Biedl, Timothy M. Chan","submitted_at":"2017-09-05T15:32:32Z","abstract_excerpt":"Let $T$ be an $n$-node tree of maximum degree 4, and let $P$ be a set of $n$ points in the plane with no two points on the same horizontal or vertical line. It is an open question whether $T$ always has a planar drawing on $P$ such that each edge is drawn as an orthogonal path with one bend (an \"L-shaped\" edge). By giving new methods for drawing trees, we improve the bounds on the size of the point set $P$ for which such drawings are possible to: $O(n^{1.55})$ for maximum degree 4 trees; $O(n^{1.22})$ for maximum degree 3 (binary) trees; and $O(n^{1.142})$ for perfect binary trees.\n  Drawing o"},"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":"1709.01456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","cross_cats_sorted":[],"title_canon_sha256":"722bd1761446da294571d3397066b467b9ea83e62dda1b4b76a0bf3ea35334ac","abstract_canon_sha256":"7551c24d32bb38f010c079499c0e4104d3d3f5aa62307780677cdeda9319dfb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:00.042493Z","signature_b64":"JJ1UnQxNtPCnbK8TaXf+zcP+G0LVNo4K+P8wD3w2yAGrfxo7QDnW2MIY4NXT50PxkCdDkT7gVo1LndfsP0h9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","last_reissued_at":"2026-05-18T00:36:00.041992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:00.041992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Kshitij Jain, Martin Derka, Therese Biedl, Timothy M. Chan","submitted_at":"2017-09-05T15:32:32Z","abstract_excerpt":"Let $T$ be an $n$-node tree of maximum degree 4, and let $P$ be a set of $n$ points in the plane with no two points on the same horizontal or vertical line. It is an open question whether $T$ always has a planar drawing on $P$ such that each edge is drawn as an orthogonal path with one bend (an \"L-shaped\" edge). By giving new methods for drawing trees, we improve the bounds on the size of the point set $P$ for which such drawings are possible to: $O(n^{1.55})$ for maximum degree 4 trees; $O(n^{1.22})$ for maximum degree 3 (binary) trees; and $O(n^{1.142})$ for perfect binary trees.\n  Drawing o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01456","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":"1709.01456","created_at":"2026-05-18T00:36:00.042061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01456v1","created_at":"2026-05-18T00:36:00.042061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01456","created_at":"2026-05-18T00:36:00.042061+00:00"},{"alias_kind":"pith_short_12","alias_value":"HCKFPCXRQPN7","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HCKFPCXRQPN7GY2A","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HCKFPCXR","created_at":"2026-05-18T12:31:18.294218+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/HCKFPCXRQPN7GY2A3YJVWTDWML","json":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML.json","graph_json":"https://pith.science/api/pith-number/HCKFPCXRQPN7GY2A3YJVWTDWML/graph.json","events_json":"https://pith.science/api/pith-number/HCKFPCXRQPN7GY2A3YJVWTDWML/events.json","paper":"https://pith.science/paper/HCKFPCXR"},"agent_actions":{"view_html":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML","download_json":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML.json","view_paper":"https://pith.science/paper/HCKFPCXR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01456&json=true","fetch_graph":"https://pith.science/api/pith-number/HCKFPCXRQPN7GY2A3YJVWTDWML/graph.json","fetch_events":"https://pith.science/api/pith-number/HCKFPCXRQPN7GY2A3YJVWTDWML/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/action/storage_attestation","attest_author":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/action/author_attestation","sign_citation":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/action/citation_signature","submit_replication":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/action/replication_record"}},"created_at":"2026-05-18T00:36:00.042061+00:00","updated_at":"2026-05-18T00:36:00.042061+00:00"}