{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MXFKX24GBTHIG4HFHYCHQTAXMC","short_pith_number":"pith:MXFKX24G","schema_version":"1.0","canonical_sha256":"65caabeb860cce8370e53e04784c17608d2363ae263a56cd9bb4187a900e119f","source":{"kind":"arxiv","id":"1504.00185","version":1},"attestation_state":"computed","paper":{"title":"Finding k partially disjoint paths in a directed planar graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver","submitted_at":"2015-04-01T11:36:09Z","abstract_excerpt":"The {\\it partially disjoint paths problem} is: {\\it given:} a directed graph, vertices $r_1,s_1,\\ldots,r_k,s_k$, and a set $F$ of pairs $\\{i,j\\}$ from $\\{1,\\ldots,k\\}$, {\\it find:} for each $i=1,\\ldots,k$ a directed $r_i-s_i$ path $P_i$ such that if $\\{i,j\\}\\in F$ then $P_i$ and $P_j$ are disjoint.\n  We show that for fixed $k$, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is solvable in polynomial time for directed graphs embedded on a fixed compact surface. Moreover, one may specify for each edge a subset of $\\{1,\\ldots,k\\}$ prescrib"},"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":"1504.00185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-01T11:36:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f2abd156fba7a56173eb6857aa3947cb5d7f2a545770148ae2ec427cf30ffaa8","abstract_canon_sha256":"6faf5dba706a3b3ab1c5403c011ce0f2303d6009909892c4d0e95cf1b59428ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:44.327942Z","signature_b64":"N1vFmTei4oU+4581Tn2TuFb3Zgfn+EA38xHVaQRwtF6LHN5LUs7ZCW/Nr57C6jZ8UsmdI1Ws2eeg9fEQ5MWeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65caabeb860cce8370e53e04784c17608d2363ae263a56cd9bb4187a900e119f","last_reissued_at":"2026-05-18T02:19:44.327426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:44.327426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding k partially disjoint paths in a directed planar graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver","submitted_at":"2015-04-01T11:36:09Z","abstract_excerpt":"The {\\it partially disjoint paths problem} is: {\\it given:} a directed graph, vertices $r_1,s_1,\\ldots,r_k,s_k$, and a set $F$ of pairs $\\{i,j\\}$ from $\\{1,\\ldots,k\\}$, {\\it find:} for each $i=1,\\ldots,k$ a directed $r_i-s_i$ path $P_i$ such that if $\\{i,j\\}\\in F$ then $P_i$ and $P_j$ are disjoint.\n  We show that for fixed $k$, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is solvable in polynomial time for directed graphs embedded on a fixed compact surface. 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