{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:J4PMC4KOL5DJT72GEZSCEHUGLV","short_pith_number":"pith:J4PMC4KO","schema_version":"1.0","canonical_sha256":"4f1ec1714e5f4699ff462664221e865d5de4bb866b5e1e7cfd7428946cc15e88","source":{"kind":"arxiv","id":"1603.08073","version":2},"attestation_state":"computed","paper":{"title":"Shortest (A+B)-path packing via hafnian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai, Hiroyuki Namba","submitted_at":"2016-03-26T04:42:17Z","abstract_excerpt":"Bj\\\"orklund and Husfeldt developed a randomized polynomial time algorithm to solve the shortest two disjoint paths problem. Their algorithm is based on computation of permanents modulo 4 and the isolation lemma. In this paper, we consider the following generalization of the shortest two disjoint paths problem, and develop a similar algebraic algorithm. The shortest perfect $(A+B)$-path packing problem is: given an undirected graph $G$ and two disjoint node subsets $A,B$ with even cardinalities, find a shortest $|A|/2+|B|/2$ disjoint paths whose ends are both in $A$ or both in $B$. Besides its "},"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":"1603.08073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-26T04:42:17Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"c3429df74f6dd5930e10770677fbc07571c4d93e1cf54b44a846416269814286","abstract_canon_sha256":"d02c5c7683b9f07687d591a222fbd0784f05150865b81ddaabc89f40a9a55291"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:33.061766Z","signature_b64":"2rT7KYrUJhORZU9zTE6ntGg3YeI6XMfrthewy9/WwSlksNGgFI+i+vC99Bq/rIkcl7/EhNWjNevdBzYHgqqRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f1ec1714e5f4699ff462664221e865d5de4bb866b5e1e7cfd7428946cc15e88","last_reissued_at":"2026-05-18T00:42:33.061000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:33.061000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shortest (A+B)-path packing via hafnian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai, Hiroyuki Namba","submitted_at":"2016-03-26T04:42:17Z","abstract_excerpt":"Bj\\\"orklund and Husfeldt developed a randomized polynomial time algorithm to solve the shortest two disjoint paths problem. Their algorithm is based on computation of permanents modulo 4 and the isolation lemma. In this paper, we consider the following generalization of the shortest two disjoint paths problem, and develop a similar algebraic algorithm. The shortest perfect $(A+B)$-path packing problem is: given an undirected graph $G$ and two disjoint node subsets $A,B$ with even cardinalities, find a shortest $|A|/2+|B|/2$ disjoint paths whose ends are both in $A$ or both in $B$. Besides its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08073","kind":"arxiv","version":2},"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":"1603.08073","created_at":"2026-05-18T00:42:33.061112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08073v2","created_at":"2026-05-18T00:42:33.061112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08073","created_at":"2026-05-18T00:42:33.061112+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4PMC4KOL5DJ","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4PMC4KOL5DJT72G","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4PMC4KO","created_at":"2026-05-18T12:30:22.444734+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/J4PMC4KOL5DJT72GEZSCEHUGLV","json":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV.json","graph_json":"https://pith.science/api/pith-number/J4PMC4KOL5DJT72GEZSCEHUGLV/graph.json","events_json":"https://pith.science/api/pith-number/J4PMC4KOL5DJT72GEZSCEHUGLV/events.json","paper":"https://pith.science/paper/J4PMC4KO"},"agent_actions":{"view_html":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV","download_json":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV.json","view_paper":"https://pith.science/paper/J4PMC4KO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08073&json=true","fetch_graph":"https://pith.science/api/pith-number/J4PMC4KOL5DJT72GEZSCEHUGLV/graph.json","fetch_events":"https://pith.science/api/pith-number/J4PMC4KOL5DJT72GEZSCEHUGLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV/action/storage_attestation","attest_author":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV/action/author_attestation","sign_citation":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV/action/citation_signature","submit_replication":"https://pith.science/pith/J4PMC4KOL5DJT72GEZSCEHUGLV/action/replication_record"}},"created_at":"2026-05-18T00:42:33.061112+00:00","updated_at":"2026-05-18T00:42:33.061112+00:00"}