{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MWENMJ2PFPHY44PLGGOF7XBG4R","short_pith_number":"pith:MWENMJ2P","schema_version":"1.0","canonical_sha256":"6588d6274f2bcf8e71eb319c5fdc26e4443728f328ad4ab98122d1270f8dec9e","source":{"kind":"arxiv","id":"1204.1616","version":2},"attestation_state":"computed","paper":{"title":"Algorithmic Applications of Baur-Strassen's Theorem: Shortest Cycles, Diameter and Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Harold N. Gabow, Marek Cygan, Piotr Sankowski","submitted_at":"2012-04-07T09:54:25Z","abstract_excerpt":"Consider a directed or an undirected graph with integral edge weights from the set [-W, W], that does not contain negative weight cycles. In this paper, we introduce a general framework for solving problems on such graphs using matrix multiplication. The framework is based on the usage of Baur-Strassen's theorem and of Strojohann's determinant algorithm. It allows us to give new and simple solutions to the following problems:\n  * Finding Shortest Cycles -- We give a simple \\tilde{O}(Wn^{\\omega}) time algorithm for finding shortest cycles in undirected and directed graphs. For directed graphs ("},"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":"1204.1616","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-04-07T09:54:25Z","cross_cats_sorted":[],"title_canon_sha256":"236987ebff6eb98de3c987aa3e32e9dc331365116e1c4b7e3a3578c92e1e5bc1","abstract_canon_sha256":"79a727343cc574caa4974b356dfc8ea43c1ac831d67b45514debb9ea4bcf25bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.382231Z","signature_b64":"XrRpJgegFw6DlaZQHJo1LuZ+2XrZuoy9q5gKEt+2C9N32qRuCGxPbbziWm+dyXqMmF6Vy9U1VsXeYGJEzlM4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6588d6274f2bcf8e71eb319c5fdc26e4443728f328ad4ab98122d1270f8dec9e","last_reissued_at":"2026-05-18T03:48:35.381725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.381725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithmic Applications of Baur-Strassen's Theorem: Shortest Cycles, Diameter and Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Harold N. Gabow, Marek Cygan, Piotr Sankowski","submitted_at":"2012-04-07T09:54:25Z","abstract_excerpt":"Consider a directed or an undirected graph with integral edge weights from the set [-W, W], that does not contain negative weight cycles. In this paper, we introduce a general framework for solving problems on such graphs using matrix multiplication. The framework is based on the usage of Baur-Strassen's theorem and of Strojohann's determinant algorithm. It allows us to give new and simple solutions to the following problems:\n  * Finding Shortest Cycles -- We give a simple \\tilde{O}(Wn^{\\omega}) time algorithm for finding shortest cycles in undirected and directed graphs. For directed graphs ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1616","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":"1204.1616","created_at":"2026-05-18T03:48:35.381805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1616v2","created_at":"2026-05-18T03:48:35.381805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1616","created_at":"2026-05-18T03:48:35.381805+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWENMJ2PFPHY","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWENMJ2PFPHY44PL","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWENMJ2P","created_at":"2026-05-18T12:27:14.488303+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/MWENMJ2PFPHY44PLGGOF7XBG4R","json":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R.json","graph_json":"https://pith.science/api/pith-number/MWENMJ2PFPHY44PLGGOF7XBG4R/graph.json","events_json":"https://pith.science/api/pith-number/MWENMJ2PFPHY44PLGGOF7XBG4R/events.json","paper":"https://pith.science/paper/MWENMJ2P"},"agent_actions":{"view_html":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R","download_json":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R.json","view_paper":"https://pith.science/paper/MWENMJ2P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1616&json=true","fetch_graph":"https://pith.science/api/pith-number/MWENMJ2PFPHY44PLGGOF7XBG4R/graph.json","fetch_events":"https://pith.science/api/pith-number/MWENMJ2PFPHY44PLGGOF7XBG4R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R/action/storage_attestation","attest_author":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R/action/author_attestation","sign_citation":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R/action/citation_signature","submit_replication":"https://pith.science/pith/MWENMJ2PFPHY44PLGGOF7XBG4R/action/replication_record"}},"created_at":"2026-05-18T03:48:35.381805+00:00","updated_at":"2026-05-18T03:48:35.381805+00:00"}