{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TX2GXFPI7JFGBMHW5RTR32Y3GD","short_pith_number":"pith:TX2GXFPI","schema_version":"1.0","canonical_sha256":"9df46b95e8fa4a60b0f6ec671deb1b30c75cd95ede33d05088f820ca80a67723","source":{"kind":"arxiv","id":"1909.00171","version":1},"attestation_state":"computed","paper":{"title":"Near-optimal Approximate Discrete and Continuous Submodular Function Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Brian Axelrod, Yang P. Liu","submitted_at":"2019-08-31T09:09:08Z","abstract_excerpt":"In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range $[-1, 1]$, computes an $\\epsilon$-additive approximate minimizer in $\\tilde{O}(n/\\epsilon^2)$ oracle evaluations with high probability. This improves over the $\\tilde{O}(n^{5/3}/\\epsilon^2)$ oracle evaluation algorithm of Chakrabarty \\etal~(STOC 2017) and the $\\tilde{O}(n^{3/2}/\\epsilon^2)$ oracle evaluation algorithm of Hamoudi \\etal.\n  Further, we leverage a"},"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":"1909.00171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-31T09:09:08Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4f7520f2c79736cd1839a68f59dc1141ef65e702906b57c649e53a04ed552e4d","abstract_canon_sha256":"97e53990f90604f5445dbed857415a0b701863ad257f288002a90e6ecf8c7be8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:03:17.562861Z","signature_b64":"ptdiiGI/cUvVxs6QAx+8sqU0QO/S+Tb72iH1pYL3eLm/jDDIh8t48KB9QwB13cPelMD+xAp0huTra3D8t4t+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9df46b95e8fa4a60b0f6ec671deb1b30c75cd95ede33d05088f820ca80a67723","last_reissued_at":"2026-07-05T00:03:17.562449Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:03:17.562449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Near-optimal Approximate Discrete and Continuous Submodular Function Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Brian Axelrod, Yang P. Liu","submitted_at":"2019-08-31T09:09:08Z","abstract_excerpt":"In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range $[-1, 1]$, computes an $\\epsilon$-additive approximate minimizer in $\\tilde{O}(n/\\epsilon^2)$ oracle evaluations with high probability. This improves over the $\\tilde{O}(n^{5/3}/\\epsilon^2)$ oracle evaluation algorithm of Chakrabarty \\etal~(STOC 2017) and the $\\tilde{O}(n^{3/2}/\\epsilon^2)$ oracle evaluation algorithm of Hamoudi \\etal.\n  Further, we leverage a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00171/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.00171","created_at":"2026-07-05T00:03:17.562508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.00171v1","created_at":"2026-07-05T00:03:17.562508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00171","created_at":"2026-07-05T00:03:17.562508+00:00"},{"alias_kind":"pith_short_12","alias_value":"TX2GXFPI7JFG","created_at":"2026-07-05T00:03:17.562508+00:00"},{"alias_kind":"pith_short_16","alias_value":"TX2GXFPI7JFGBMHW","created_at":"2026-07-05T00:03:17.562508+00:00"},{"alias_kind":"pith_short_8","alias_value":"TX2GXFPI","created_at":"2026-07-05T00:03:17.562508+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/TX2GXFPI7JFGBMHW5RTR32Y3GD","json":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD.json","graph_json":"https://pith.science/api/pith-number/TX2GXFPI7JFGBMHW5RTR32Y3GD/graph.json","events_json":"https://pith.science/api/pith-number/TX2GXFPI7JFGBMHW5RTR32Y3GD/events.json","paper":"https://pith.science/paper/TX2GXFPI"},"agent_actions":{"view_html":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD","download_json":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD.json","view_paper":"https://pith.science/paper/TX2GXFPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.00171&json=true","fetch_graph":"https://pith.science/api/pith-number/TX2GXFPI7JFGBMHW5RTR32Y3GD/graph.json","fetch_events":"https://pith.science/api/pith-number/TX2GXFPI7JFGBMHW5RTR32Y3GD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD/action/storage_attestation","attest_author":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD/action/author_attestation","sign_citation":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD/action/citation_signature","submit_replication":"https://pith.science/pith/TX2GXFPI7JFGBMHW5RTR32Y3GD/action/replication_record"}},"created_at":"2026-07-05T00:03:17.562508+00:00","updated_at":"2026-07-05T00:03:17.562508+00:00"}