{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F6V6IBU4QGVTY6G6F5ROQLB3IJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"046d3e418bd8b80415dfedd76734011efe23c8d753d78881d0a0ffb914d062f5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-23T19:38:56Z","title_canon_sha256":"250041b4a7359bfc1986d7c188617cf3654809b189a697ee5a4deba6dbe5f47e"},"schema_version":"1.0","source":{"id":"1105.4593","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4593","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4593v5","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4593","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"F6V6IBU4QGVT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6V6IBU4QGVTY6G6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6V6IBU4","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:e0b67e8cdd0de81d128cb426ef1d0e0ebae2c95b58014ed80256cec22b300de8","target":"graph","created_at":"2026-05-18T02:45:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the problem of maximizing a non-negative submodular set function $f:2^N \\rightarrow \\mathbb{R}_+$ over a ground set $N$ subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general framework that allows us to derive a number of new results, in particular when $f$ may be a non-monotone function. Our algorithms are based on (approximately) maximizing the multilinear extension $F$ of $f$ over a polytope $P$ that represents the constraints, and then effectively rounding the f","authors_text":"Chandra Chekuri, Jan Vondr\\'ak, Rico Zenklusen","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-23T19:38:56Z","title":"Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4593","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c52532ba6da3cf7ad7d158d6dfa77a83200c357189f2948e141a3a1125cbabba","target":"record","created_at":"2026-05-18T02:45:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"046d3e418bd8b80415dfedd76734011efe23c8d753d78881d0a0ffb914d062f5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-23T19:38:56Z","title_canon_sha256":"250041b4a7359bfc1986d7c188617cf3654809b189a697ee5a4deba6dbe5f47e"},"schema_version":"1.0","source":{"id":"1105.4593","kind":"arxiv","version":5}},"canonical_sha256":"2fabe4069c81ab3c78de2f62e82c3b427d66dfa3ee559f671f22dcff6fca43cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fabe4069c81ab3c78de2f62e82c3b427d66dfa3ee559f671f22dcff6fca43cf","first_computed_at":"2026-05-18T02:45:21.748090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.748090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y8p8nJM+uBBSbAinaUNlC+0ia0KqC3X1ZgyYIU+mNSYcJryPsL5gPD/avhDQpbIGnDKtaBeeRdhs+h5YSw2BAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.748731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4593","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c52532ba6da3cf7ad7d158d6dfa77a83200c357189f2948e141a3a1125cbabba","sha256:e0b67e8cdd0de81d128cb426ef1d0e0ebae2c95b58014ed80256cec22b300de8"],"state_sha256":"3084a14181f26f559ac7790cdc403cc14c0ba243f32e41194c946436804f3fd0"}