{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BX6CTH4VCNVVVHXYW7MEE2RWVL","short_pith_number":"pith:BX6CTH4V","schema_version":"1.0","canonical_sha256":"0dfc299f95136b5a9ef8b7d8426a36aac4d9cd792610731e2604cbe56f8726c9","source":{"kind":"arxiv","id":"1304.4207","version":1},"attestation_state":"computed","paper":{"title":"The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"D\\'aniel Marx, Marcin Pilipczuk, Marek Cygan, Micha{\\l} Pilipczuk","submitted_at":"2013-04-15T19:15:18Z","abstract_excerpt":"Given a graph G and k pairs of vertices (s_1,t_1), ..., (s_k,t_k), the k-Vertex-Disjoint Paths problem asks for pairwise vertex-disjoint paths P_1, ..., P_k such that P_i goes from s_i to t_i. Schrijver [SICOMP'94] proved that the k-Vertex-Disjoint Paths problem on planar directed graphs can be solved in time n^{O(k)}. We give an algorithm with running time 2^{2^{O(k^2)}} n^{O(1)} for the problem, that is, we show the fixed-parameter tractability of the problem."},"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":"1304.4207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-15T19:15:18Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"fc087fb0c529a823829b00ec459951c8038e50544d3db7c5175dad843d802a1c","abstract_canon_sha256":"0dea38e6577eb5a392f5e6b9d980b4727225b8f8c28ab139374e58d7bcfb8b76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:55.161627Z","signature_b64":"muzivM+iqB4udNkvlaosEqAeH43MCPEqZFT/igRFsfwoAH6TWnAI9mlNm87388qFnAV/d4cWjLWMRlOVL10cAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dfc299f95136b5a9ef8b7d8426a36aac4d9cd792610731e2604cbe56f8726c9","last_reissued_at":"2026-05-18T03:27:55.160869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:55.160869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"D\\'aniel Marx, Marcin Pilipczuk, Marek Cygan, Micha{\\l} Pilipczuk","submitted_at":"2013-04-15T19:15:18Z","abstract_excerpt":"Given a graph G and k pairs of vertices (s_1,t_1), ..., (s_k,t_k), the k-Vertex-Disjoint Paths problem asks for pairwise vertex-disjoint paths P_1, ..., P_k such that P_i goes from s_i to t_i. Schrijver [SICOMP'94] proved that the k-Vertex-Disjoint Paths problem on planar directed graphs can be solved in time n^{O(k)}. We give an algorithm with running time 2^{2^{O(k^2)}} n^{O(1)} for the problem, that is, we show the fixed-parameter tractability of the problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4207","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":"1304.4207","created_at":"2026-05-18T03:27:55.161000+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4207v1","created_at":"2026-05-18T03:27:55.161000+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4207","created_at":"2026-05-18T03:27:55.161000+00:00"},{"alias_kind":"pith_short_12","alias_value":"BX6CTH4VCNVV","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BX6CTH4VCNVVVHXY","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BX6CTH4V","created_at":"2026-05-18T12:27:40.988391+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/BX6CTH4VCNVVVHXYW7MEE2RWVL","json":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL.json","graph_json":"https://pith.science/api/pith-number/BX6CTH4VCNVVVHXYW7MEE2RWVL/graph.json","events_json":"https://pith.science/api/pith-number/BX6CTH4VCNVVVHXYW7MEE2RWVL/events.json","paper":"https://pith.science/paper/BX6CTH4V"},"agent_actions":{"view_html":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL","download_json":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL.json","view_paper":"https://pith.science/paper/BX6CTH4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4207&json=true","fetch_graph":"https://pith.science/api/pith-number/BX6CTH4VCNVVVHXYW7MEE2RWVL/graph.json","fetch_events":"https://pith.science/api/pith-number/BX6CTH4VCNVVVHXYW7MEE2RWVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL/action/storage_attestation","attest_author":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL/action/author_attestation","sign_citation":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL/action/citation_signature","submit_replication":"https://pith.science/pith/BX6CTH4VCNVVVHXYW7MEE2RWVL/action/replication_record"}},"created_at":"2026-05-18T03:27:55.161000+00:00","updated_at":"2026-05-18T03:27:55.161000+00:00"}