{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UA7ABQV3P5AI53D3DLII27SV5F","short_pith_number":"pith:UA7ABQV3","schema_version":"1.0","canonical_sha256":"a03e00c2bb7f408eec7b1ad08d7e55e972eeb2c99b1f5ef2dff599a9feda1879","source":{"kind":"arxiv","id":"2106.07116","version":2},"attestation_state":"computed","paper":{"title":"The Power of Randomization: Efficient and Effective Algorithms for Constrained Submodular Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Benwei Wu, He Huang, Jing Tang, Kai Han, Shuang Cui, Tianshuai Zhu","submitted_at":"2021-06-14T00:14:36Z","abstract_excerpt":"Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which generalizes many other important constraints in submodular optimization such as cardinality constraint, matroid constraint, and $k$-extendible system constraint. The existing approaches for this problem achieve the best-known approximation ratio of $k+2\\sqrt{k+2}+3$ (for a general submodular function) based on deterministic algorithmic frameworks. We propose several"},"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":"2106.07116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-06-14T00:14:36Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"da58b47cec00b3a36df652664345915bdacd4c85d97a98ee2a614f5c0f8fead0","abstract_canon_sha256":"6ba760c9a53bd51db27af88a8fb5c3db1b57690d6c6c3dcd0f61da221a96d764"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:49:32.482298Z","signature_b64":"yyYDAEKeIx0M4UPo/DDHUC1qHpf85SnB2eSnXJUD2YKmLE5j79NvD1we5RUFNzI+MvKp1gmWof7id89Tm8mkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a03e00c2bb7f408eec7b1ad08d7e55e972eeb2c99b1f5ef2dff599a9feda1879","last_reissued_at":"2026-07-05T02:49:32.481825Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:49:32.481825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Power of Randomization: Efficient and Effective Algorithms for Constrained Submodular Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Benwei Wu, He Huang, Jing Tang, Kai Han, Shuang Cui, Tianshuai Zhu","submitted_at":"2021-06-14T00:14:36Z","abstract_excerpt":"Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which generalizes many other important constraints in submodular optimization such as cardinality constraint, matroid constraint, and $k$-extendible system constraint. The existing approaches for this problem achieve the best-known approximation ratio of $k+2\\sqrt{k+2}+3$ (for a general submodular function) based on deterministic algorithmic frameworks. We propose several"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07116","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.07116/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":"2106.07116","created_at":"2026-07-05T02:49:32.481877+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.07116v2","created_at":"2026-07-05T02:49:32.481877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.07116","created_at":"2026-07-05T02:49:32.481877+00:00"},{"alias_kind":"pith_short_12","alias_value":"UA7ABQV3P5AI","created_at":"2026-07-05T02:49:32.481877+00:00"},{"alias_kind":"pith_short_16","alias_value":"UA7ABQV3P5AI53D3","created_at":"2026-07-05T02:49:32.481877+00:00"},{"alias_kind":"pith_short_8","alias_value":"UA7ABQV3","created_at":"2026-07-05T02:49:32.481877+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/UA7ABQV3P5AI53D3DLII27SV5F","json":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F.json","graph_json":"https://pith.science/api/pith-number/UA7ABQV3P5AI53D3DLII27SV5F/graph.json","events_json":"https://pith.science/api/pith-number/UA7ABQV3P5AI53D3DLII27SV5F/events.json","paper":"https://pith.science/paper/UA7ABQV3"},"agent_actions":{"view_html":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F","download_json":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F.json","view_paper":"https://pith.science/paper/UA7ABQV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.07116&json=true","fetch_graph":"https://pith.science/api/pith-number/UA7ABQV3P5AI53D3DLII27SV5F/graph.json","fetch_events":"https://pith.science/api/pith-number/UA7ABQV3P5AI53D3DLII27SV5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F/action/storage_attestation","attest_author":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F/action/author_attestation","sign_citation":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F/action/citation_signature","submit_replication":"https://pith.science/pith/UA7ABQV3P5AI53D3DLII27SV5F/action/replication_record"}},"created_at":"2026-07-05T02:49:32.481877+00:00","updated_at":"2026-07-05T02:49:32.481877+00:00"}