{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OBTXEYMXLZLIYPBY3JXW2X5B7H","short_pith_number":"pith:OBTXEYMX","schema_version":"1.0","canonical_sha256":"70677261975e568c3c38da6f6d5fa1f9cd07c49d0a3713bd7507e2cdb5c237a4","source":{"kind":"arxiv","id":"1606.02233","version":1},"attestation_state":"computed","paper":{"title":"Order-preserving drawings of trees with approximately optimal height (and small width)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Johannes Batzill, Therese Biedl","submitted_at":"2016-06-07T17:52:57Z","abstract_excerpt":"In this paper, we study how to draw trees so that they are planar, straight-line and respect a given order of edges around each node. We focus on minimizing the height, and show that we can always achieve a height of at most 2pw(T)+1, where pw(T) (the so-called pathwidth) is a known lower bound on the height. Hence we give an asymptotic 2-approximation algorithm. We also create a drawing whose height is at most 3pw(T ), but where the width can be bounded by the number of nodes. Finally we construct trees that require height 2pw(T)+1 in all planar order-preserving straight-line drawings."},"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":"1606.02233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-06-07T17:52:57Z","cross_cats_sorted":[],"title_canon_sha256":"2a30d6645c1ecc1300998af75beee349d30832bc4928feaa83dc399b0e4ab10c","abstract_canon_sha256":"70c497d05dca58313c0e03c5c2239bbd0880fbb0bc85b4d0ca2a767a5e8df77d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:44.420363Z","signature_b64":"/ggVPjq8omGiWRk9h3+p6Wwlgv4u8tZe2ACRoG6vK5sWPFtHdxlI0RBdhD3qZhTlCFYOJmUpdGWWJbiuLZVdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70677261975e568c3c38da6f6d5fa1f9cd07c49d0a3713bd7507e2cdb5c237a4","last_reissued_at":"2026-05-18T01:12:44.419956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:44.419956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Order-preserving drawings of trees with approximately optimal height (and small width)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Johannes Batzill, Therese Biedl","submitted_at":"2016-06-07T17:52:57Z","abstract_excerpt":"In this paper, we study how to draw trees so that they are planar, straight-line and respect a given order of edges around each node. We focus on minimizing the height, and show that we can always achieve a height of at most 2pw(T)+1, where pw(T) (the so-called pathwidth) is a known lower bound on the height. Hence we give an asymptotic 2-approximation algorithm. We also create a drawing whose height is at most 3pw(T ), but where the width can be bounded by the number of nodes. Finally we construct trees that require height 2pw(T)+1 in all planar order-preserving straight-line drawings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02233","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":"1606.02233","created_at":"2026-05-18T01:12:44.420020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02233v1","created_at":"2026-05-18T01:12:44.420020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02233","created_at":"2026-05-18T01:12:44.420020+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBTXEYMXLZLI","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBTXEYMXLZLIYPBY","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBTXEYMX","created_at":"2026-05-18T12:30:36.002864+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/OBTXEYMXLZLIYPBY3JXW2X5B7H","json":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H.json","graph_json":"https://pith.science/api/pith-number/OBTXEYMXLZLIYPBY3JXW2X5B7H/graph.json","events_json":"https://pith.science/api/pith-number/OBTXEYMXLZLIYPBY3JXW2X5B7H/events.json","paper":"https://pith.science/paper/OBTXEYMX"},"agent_actions":{"view_html":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H","download_json":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H.json","view_paper":"https://pith.science/paper/OBTXEYMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02233&json=true","fetch_graph":"https://pith.science/api/pith-number/OBTXEYMXLZLIYPBY3JXW2X5B7H/graph.json","fetch_events":"https://pith.science/api/pith-number/OBTXEYMXLZLIYPBY3JXW2X5B7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H/action/storage_attestation","attest_author":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H/action/author_attestation","sign_citation":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H/action/citation_signature","submit_replication":"https://pith.science/pith/OBTXEYMXLZLIYPBY3JXW2X5B7H/action/replication_record"}},"created_at":"2026-05-18T01:12:44.420020+00:00","updated_at":"2026-05-18T01:12:44.420020+00:00"}