{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CNTCMVX52RRKBMZKDQH5EXZL6N","short_pith_number":"pith:CNTCMVX5","schema_version":"1.0","canonical_sha256":"13662656fdd462a0b32a1c0fd25f2bf3579c6546906945917d4dbf03a06b9354","source":{"kind":"arxiv","id":"1708.09515","version":1},"attestation_state":"computed","paper":{"title":"On Upward Drawings of Trees on a Given Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Debajyoti Mondal, Therese Biedl","submitted_at":"2017-08-31T00:59:02Z","abstract_excerpt":"Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded.\n  In this paper we take a major step in understanding the complexity of "},"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":"1708.09515","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-31T00:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"691128e2f77ee3c0546db8a2b93f37d585422d97e6c612b16252e9a549b19703","abstract_canon_sha256":"c6c01a8871475ebbb6596debd79c0b74623f331f840aae4b54105a9294de1065"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:18.546879Z","signature_b64":"WMJGV8K1sjqapUejsD7ZnNkfS57whzrw60S4zO2S6lmnKLclMbHacGqewLfgH0juyD+yKPjdx87E17jjxUMWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13662656fdd462a0b32a1c0fd25f2bf3579c6546906945917d4dbf03a06b9354","last_reissued_at":"2026-05-18T00:36:18.546238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:18.546238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Upward Drawings of Trees on a Given Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Debajyoti Mondal, Therese Biedl","submitted_at":"2017-08-31T00:59:02Z","abstract_excerpt":"Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded.\n  In this paper we take a major step in understanding the complexity of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09515","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":"1708.09515","created_at":"2026-05-18T00:36:18.546362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.09515v1","created_at":"2026-05-18T00:36:18.546362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09515","created_at":"2026-05-18T00:36:18.546362+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNTCMVX52RRK","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNTCMVX52RRKBMZK","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNTCMVX5","created_at":"2026-05-18T12:31:10.602751+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/CNTCMVX52RRKBMZKDQH5EXZL6N","json":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N.json","graph_json":"https://pith.science/api/pith-number/CNTCMVX52RRKBMZKDQH5EXZL6N/graph.json","events_json":"https://pith.science/api/pith-number/CNTCMVX52RRKBMZKDQH5EXZL6N/events.json","paper":"https://pith.science/paper/CNTCMVX5"},"agent_actions":{"view_html":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N","download_json":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N.json","view_paper":"https://pith.science/paper/CNTCMVX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.09515&json=true","fetch_graph":"https://pith.science/api/pith-number/CNTCMVX52RRKBMZKDQH5EXZL6N/graph.json","fetch_events":"https://pith.science/api/pith-number/CNTCMVX52RRKBMZKDQH5EXZL6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N/action/storage_attestation","attest_author":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N/action/author_attestation","sign_citation":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N/action/citation_signature","submit_replication":"https://pith.science/pith/CNTCMVX52RRKBMZKDQH5EXZL6N/action/replication_record"}},"created_at":"2026-05-18T00:36:18.546362+00:00","updated_at":"2026-05-18T00:36:18.546362+00:00"}