{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HHYTHAHPVZC7FD6Q2L6D3ADDZ3","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":"d392f8abfe61ee2533a2e860d621f596d6a34b3aa59ca5f0fa128a0ed9494969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-10T19:54:40Z","title_canon_sha256":"e50ba6cbb5795c316dbb1fc214350472fa06cb0503afbd38d2261885e1987454"},"schema_version":"1.0","source":{"id":"2002.04063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.04063","created_at":"2026-07-05T00:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"2002.04063v1","created_at":"2026-07-05T00:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.04063","created_at":"2026-07-05T00:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"HHYTHAHPVZC7","created_at":"2026-07-05T00:39:41Z"},{"alias_kind":"pith_short_16","alias_value":"HHYTHAHPVZC7FD6Q","created_at":"2026-07-05T00:39:41Z"},{"alias_kind":"pith_short_8","alias_value":"HHYTHAHP","created_at":"2026-07-05T00:39:41Z"}],"graph_snapshots":[{"event_id":"sha256:550be3b0a1a2a935ed32491f6f864b79eee2171ace8ea3251cc62e387203b79d","target":"graph","created_at":"2026-07-05T00:39:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.04063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of 1-1/e when maximizing a monotone submodular function under a cardinality constraint. However, empirical studies show that its performance is substantially better in practice. This raises a natural question of explaining this improved performance of the greedy algorithm. In this work, we define sharpness for submodular functions as a candidate explanation for ","authors_text":"Alfredo Torrico, Mohit Singh, Sebastian Pokutta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-10T19:54:40Z","title":"On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts to Sharpness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.04063","kind":"arxiv","version":1},"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:ed02e4dd4da6540eb7bcd5fcb449cc44f315591e7540b1567ad419e96beda903","target":"record","created_at":"2026-07-05T00:39:41Z","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":"d392f8abfe61ee2533a2e860d621f596d6a34b3aa59ca5f0fa128a0ed9494969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-10T19:54:40Z","title_canon_sha256":"e50ba6cbb5795c316dbb1fc214350472fa06cb0503afbd38d2261885e1987454"},"schema_version":"1.0","source":{"id":"2002.04063","kind":"arxiv","version":1}},"canonical_sha256":"39f13380efae45f28fd0d2fc3d8063cec82feec4b0d1b1b0dbc6e45d2cd97230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39f13380efae45f28fd0d2fc3d8063cec82feec4b0d1b1b0dbc6e45d2cd97230","first_computed_at":"2026-07-05T00:39:41.823840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:41.823840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0h5vGVhYlBR1XC52a5FxIqcqWhs236sMUWO8yarCLGMSYMG0gDuN0UBht/6B7BYBrh5WAqS+OV0Zj7fB6UP4Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:41.824371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.04063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed02e4dd4da6540eb7bcd5fcb449cc44f315591e7540b1567ad419e96beda903","sha256:550be3b0a1a2a935ed32491f6f864b79eee2171ace8ea3251cc62e387203b79d"],"state_sha256":"406679964bb287757169a6887ab06635ec0480f04f76cbc53a00d69ef94c4c1c"}