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The best previously known algorithm for the former problem, running in $O(n\\log^3 n)$ time, can be obtained from the algorithm of \\Lacki, Nussbaum, Sankowski, and Wulff-Nilsen for single-source all-sinks maximum flows. The best previously known result for the latter problem is the $O(n\\log^3 n)$-time algorithm of Wulff-Nilsen. By exploiting duality between the two problems in pla"},"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":"1703.07964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-23T08:37:54Z","cross_cats_sorted":[],"title_canon_sha256":"32f633e5f12fc66ddc7b8379609347d9e9e2a0fb76d7f25573dc084cb0679361","abstract_canon_sha256":"66b14e47fdd9767befc77ce766db91acdd4950e3e19963968c35c161a9b16c04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:04.282031Z","signature_b64":"muvPr8m97BwapbivffHipgwIfv8/JZ+efVKoM2FaOnEcRhs08uDEEJmKhzpu1lla0o47mWKNG4OfOBqFbNoqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"606d9098523352c98a957b3053b91948612d579eb7d6cff82dcd270e62c17f08","last_reissued_at":"2026-05-18T00:48:04.281437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:04.281437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum Cuts and Shortest Cycles in Directed Planar Graphs via Noncrossing Shortest Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hsueh-I Lu, Hung-Chun Liang","submitted_at":"2017-03-23T08:37:54Z","abstract_excerpt":"Let $G$ be an $n$-node simple directed planar graph with nonnegative edge weights. 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