{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XNEL5GQWNAQJ7KPEDZPXZJQK7R","short_pith_number":"pith:XNEL5GQW","schema_version":"1.0","canonical_sha256":"bb48be9a1668209fa9e41e5f7ca60afc76bc34f65ca5123b6d8d648186482a76","source":{"kind":"arxiv","id":"2607.05759","version":1},"attestation_state":"computed","paper":{"title":"Data-dependent Evaluations for Budgeted Submodular Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.DM"],"primary_cat":"cs.DS","authors_text":"Jing Tang, Lejian Zhang, Xueyan Tang","submitted_at":"2026-07-07T02:34:10Z","abstract_excerpt":"Submodular maximization is an important building block for developing algorithms in many areas such as machine learning and data mining. Due to the NP-hardness of the problem, analysis of submodular maximization algorithms typically provides pessimistic worst-case approximation factors only. It is not easy to evaluate how close a produced solution is to an optimal one for a given problem instance. In this paper, we develop new data-dependent upper bounds for submodular maximization with a knapsack constraint. We theoretically prove that they dominate the optimal solution and empirically demons"},"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":"2607.05759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T02:34:10Z","cross_cats_sorted":["cs.AI","cs.DM"],"title_canon_sha256":"435f049af8a7012022d1de2f802bc7db4a7e457492fe0dcf17fe90054028f96b","abstract_canon_sha256":"4a9908446782e1f770966bcc775a2445a56ec010f32e96a406f8b38c7425b70b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:44.066710Z","signature_b64":"d+bkJ+9+/x+SZE+QulHvXGJJHJrLiMP9N44j9qkL/lPN3KbZaqVeWQg5sK6u+PIRIX1tMzkbwtFz7Ii2BkBWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb48be9a1668209fa9e41e5f7ca60afc76bc34f65ca5123b6d8d648186482a76","last_reissued_at":"2026-07-08T01:18:44.066260Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:44.066260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Data-dependent Evaluations for Budgeted Submodular Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.DM"],"primary_cat":"cs.DS","authors_text":"Jing Tang, Lejian Zhang, Xueyan Tang","submitted_at":"2026-07-07T02:34:10Z","abstract_excerpt":"Submodular maximization is an important building block for developing algorithms in many areas such as machine learning and data mining. Due to the NP-hardness of the problem, analysis of submodular maximization algorithms typically provides pessimistic worst-case approximation factors only. It is not easy to evaluate how close a produced solution is to an optimal one for a given problem instance. In this paper, we develop new data-dependent upper bounds for submodular maximization with a knapsack constraint. We theoretically prove that they dominate the optimal solution and empirically demons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05759","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/2607.05759/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":"2607.05759","created_at":"2026-07-08T01:18:44.066327+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.05759v1","created_at":"2026-07-08T01:18:44.066327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05759","created_at":"2026-07-08T01:18:44.066327+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNEL5GQWNAQJ","created_at":"2026-07-08T01:18:44.066327+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNEL5GQWNAQJ7KPE","created_at":"2026-07-08T01:18:44.066327+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNEL5GQW","created_at":"2026-07-08T01:18:44.066327+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/XNEL5GQWNAQJ7KPEDZPXZJQK7R","json":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R.json","graph_json":"https://pith.science/api/pith-number/XNEL5GQWNAQJ7KPEDZPXZJQK7R/graph.json","events_json":"https://pith.science/api/pith-number/XNEL5GQWNAQJ7KPEDZPXZJQK7R/events.json","paper":"https://pith.science/paper/XNEL5GQW"},"agent_actions":{"view_html":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R","download_json":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R.json","view_paper":"https://pith.science/paper/XNEL5GQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.05759&json=true","fetch_graph":"https://pith.science/api/pith-number/XNEL5GQWNAQJ7KPEDZPXZJQK7R/graph.json","fetch_events":"https://pith.science/api/pith-number/XNEL5GQWNAQJ7KPEDZPXZJQK7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R/action/storage_attestation","attest_author":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R/action/author_attestation","sign_citation":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R/action/citation_signature","submit_replication":"https://pith.science/pith/XNEL5GQWNAQJ7KPEDZPXZJQK7R/action/replication_record"}},"created_at":"2026-07-08T01:18:44.066327+00:00","updated_at":"2026-07-08T01:18:44.066327+00:00"}