{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZQBB2PCXZ5EFXSVLVE2L5KYEEI","short_pith_number":"pith:ZQBB2PCX","schema_version":"1.0","canonical_sha256":"cc021d3c57cf485bcaaba934beab04223dc69ee3880ee888c9374d499e5fb0ef","source":{"kind":"arxiv","id":"1907.11078","version":1},"attestation_state":"computed","paper":{"title":"Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, Karol W\\k{e}grzycki, Marvin K\\\"unnemann","submitted_at":"2019-07-25T14:14:06Z","abstract_excerpt":"Zwick's $(1+\\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\\widetilde{O}(\\frac{n^\\omega}{\\varepsilon} \\log{W})$, where $\\omega \\le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound.\n  Since Zwick's algorithm uses the scaling technique, it has a factor $\\log W$ in the running time. In this paper, we study whether APSP and related problems"},"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":"1907.11078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-25T14:14:06Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"09c93762d198477ed0d3ae33ced39f3ecd5cc12b4e9f4abef21b4d18cf006414","abstract_canon_sha256":"56b9bb0f5ddfb14811a92ee6c26d4ec49ed3d260bd903d366c0426e7b3922826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:33.549461Z","signature_b64":"TKbfSN1zlKhkE6Qy+iHHrCWwneWDrmFmxYO5sJvJxgE1R6NdpvdggEUxiQ0JGJDp0hkqPPrAzBnth9gOFimxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc021d3c57cf485bcaaba934beab04223dc69ee3880ee888c9374d499e5fb0ef","last_reissued_at":"2026-05-17T23:39:33.548814Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:33.548814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, Karol W\\k{e}grzycki, Marvin K\\\"unnemann","submitted_at":"2019-07-25T14:14:06Z","abstract_excerpt":"Zwick's $(1+\\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\\widetilde{O}(\\frac{n^\\omega}{\\varepsilon} \\log{W})$, where $\\omega \\le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound.\n  Since Zwick's algorithm uses the scaling technique, it has a factor $\\log W$ in the running time. In this paper, we study whether APSP and related problems"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11078","kind":"arxiv","version":1},"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":"1907.11078","created_at":"2026-05-17T23:39:33.548911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.11078v1","created_at":"2026-05-17T23:39:33.548911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11078","created_at":"2026-05-17T23:39:33.548911+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQBB2PCXZ5EF","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQBB2PCXZ5EFXSVL","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQBB2PCX","created_at":"2026-05-18T12:33:33.725879+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/ZQBB2PCXZ5EFXSVLVE2L5KYEEI","json":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI.json","graph_json":"https://pith.science/api/pith-number/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/graph.json","events_json":"https://pith.science/api/pith-number/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/events.json","paper":"https://pith.science/paper/ZQBB2PCX"},"agent_actions":{"view_html":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI","download_json":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI.json","view_paper":"https://pith.science/paper/ZQBB2PCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.11078&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/action/storage_attestation","attest_author":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/action/author_attestation","sign_citation":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/action/citation_signature","submit_replication":"https://pith.science/pith/ZQBB2PCXZ5EFXSVLVE2L5KYEEI/action/replication_record"}},"created_at":"2026-05-17T23:39:33.548911+00:00","updated_at":"2026-05-17T23:39:33.548911+00:00"}