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When $k$ is fixed, this gives a polynomial algorithm for the arc-disjoint paths problem under the same hypothesis."},"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":"1008.3652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-08-21T18:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"75ad078db5c1deef066b392dfe926e4dda1365daf0c78168c8f8a01be63e4df6","abstract_canon_sha256":"bb80257d45ca7f22de04941b774651b7b714765bf9d12131d275ef790a2baf6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:55.426773Z","signature_b64":"PsQoKmknCwVvrOKl/aUcuJy9y6Xwqw5kX1cMtD7NXRJaxllH+KapXqVBL8+S+W65cnSENvyLgVzNSOzqtqP4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e53d4ae2a4da0f1e463fe419833c4cea89987eebd832086fa914dd3461b183bd","last_reissued_at":"2026-05-18T04:41:55.426379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:55.426379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On disjoint paths in acyclic planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Guyslain Naves","submitted_at":"2010-08-21T18:33:15Z","abstract_excerpt":"We give an algorithm with complexity $O(f(R)^{k^2} k^3 n)$ for the integer multiflow problem on instances $(G,H,r,c)$ with $G$ an acyclic planar digraph and $r+c$ Eulerian. 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