{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DQ3J52ECEJO7MVB56K4TCSMFP7","short_pith_number":"pith:DQ3J52EC","canonical_record":{"source":{"id":"1007.3604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-21T10:23:47Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ed452fb0eca5205237cacddecf5ec6f0cf69f43540e33d5e6a48d70183b684a9","abstract_canon_sha256":"6d74805e064301fa0d0b5ccd571abb6b4f4f838d75122cf95a3c34cf9cdfbb4e"},"schema_version":"1.0"},"canonical_sha256":"1c369ee882225df6543df2b93149857fdd1f8e9d752f0b33c703dcc1bd50b99c","source":{"kind":"arxiv","id":"1007.3604","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3604","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3604v2","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3604","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"DQ3J52ECEJO7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DQ3J52ECEJO7MVB5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DQ3J52EC","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DQ3J52ECEJO7MVB56K4TCSMFP7","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-21T10:23:47Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ed452fb0eca5205237cacddecf5ec6f0cf69f43540e33d5e6a48d70183b684a9","abstract_canon_sha256":"6d74805e064301fa0d0b5ccd571abb6b4f4f838d75122cf95a3c34cf9cdfbb4e"},"schema_version":"1.0"},"canonical_sha256":"1c369ee882225df6543df2b93149857fdd1f8e9d752f0b33c703dcc1bd50b99c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:45.268195Z","signature_b64":"CIgHDgIvXYJh0Vp2qLZ7H1LlAyo7y+I5muB1lb91hP2G18miKfSK6GvFR35OGh6onj7dmGz6L5QjZgVTzgl2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c369ee882225df6543df2b93149857fdd1f8e9d752f0b33c703dcc1bd50b99c","last_reissued_at":"2026-05-18T03:56:45.267555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:45.267555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3604","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhxfksOP4D9KagYfGVEIOYRyZ7fdlNsgmUi3oTD4DArEpl9mI13YZlQdjTeNsPupoJ4/jGWmZpRe8oXrilidDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:47.005972Z"},"content_sha256":"0154bd47b89b5d66c9ba595c11f8f36b5b233f61b7766bb849a795379b769ab4","schema_version":"1.0","event_id":"sha256:0154bd47b89b5d66c9ba595c11f8f36b5b233f61b7766bb849a795379b769ab4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DQ3J52ECEJO7MVB56K4TCSMFP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Submodular Function Maximization under Linear Packing Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Iftah Gamzu, Yossi Azar","submitted_at":"2010-07-21T10:23:47Z","abstract_excerpt":"We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \\in [0,1]^{m \\times n}$, a vector $b \\in [1,\\infty)^m$, and a monotone submodular set function $f: 2^{[n]} \\rightarrow \\bbR_+$. The objective is to find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \\leq b$, where $x_S$ stands for the characteristic vector of the set $S$. A well-studied special case of this problem is when $f$ is linear. This special case captures the class of packing integer programs.\n  Our main contribution is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3604","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"govUwMfVvmU24qJlQW87YscEtUqAcsqIvw7gceXpP525pwbQW30vzANZ005XSHG7sCUO9VxFbdmf8zG227tBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:47.006610Z"},"content_sha256":"3b1746968b8fd56e413f7abe9fd917196a1dac61682075d04c2cd3f48bbb4ab7","schema_version":"1.0","event_id":"sha256:3b1746968b8fd56e413f7abe9fd917196a1dac61682075d04c2cd3f48bbb4ab7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/bundle.json","state_url":"https://pith.science/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T16:39:47Z","links":{"resolver":"https://pith.science/pith/DQ3J52ECEJO7MVB56K4TCSMFP7","bundle":"https://pith.science/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/bundle.json","state":"https://pith.science/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQ3J52ECEJO7MVB56K4TCSMFP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DQ3J52ECEJO7MVB56K4TCSMFP7","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":"6d74805e064301fa0d0b5ccd571abb6b4f4f838d75122cf95a3c34cf9cdfbb4e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-21T10:23:47Z","title_canon_sha256":"ed452fb0eca5205237cacddecf5ec6f0cf69f43540e33d5e6a48d70183b684a9"},"schema_version":"1.0","source":{"id":"1007.3604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3604","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3604v2","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3604","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"DQ3J52ECEJO7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DQ3J52ECEJO7MVB5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DQ3J52EC","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:3b1746968b8fd56e413f7abe9fd917196a1dac61682075d04c2cd3f48bbb4ab7","target":"graph","created_at":"2026-05-18T03:56:45Z","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 study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \\in [0,1]^{m \\times n}$, a vector $b \\in [1,\\infty)^m$, and a monotone submodular set function $f: 2^{[n]} \\rightarrow \\bbR_+$. The objective is to find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \\leq b$, where $x_S$ stands for the characteristic vector of the set $S$. A well-studied special case of this problem is when $f$ is linear. This special case captures the class of packing integer programs.\n  Our main contribution is ","authors_text":"Iftah Gamzu, Yossi Azar","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-21T10:23:47Z","title":"Efficient Submodular Function Maximization under Linear Packing Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3604","kind":"arxiv","version":2},"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":"sha256:0154bd47b89b5d66c9ba595c11f8f36b5b233f61b7766bb849a795379b769ab4","target":"record","created_at":"2026-05-18T03:56:45Z","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":"6d74805e064301fa0d0b5ccd571abb6b4f4f838d75122cf95a3c34cf9cdfbb4e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-21T10:23:47Z","title_canon_sha256":"ed452fb0eca5205237cacddecf5ec6f0cf69f43540e33d5e6a48d70183b684a9"},"schema_version":"1.0","source":{"id":"1007.3604","kind":"arxiv","version":2}},"canonical_sha256":"1c369ee882225df6543df2b93149857fdd1f8e9d752f0b33c703dcc1bd50b99c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c369ee882225df6543df2b93149857fdd1f8e9d752f0b33c703dcc1bd50b99c","first_computed_at":"2026-05-18T03:56:45.267555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:45.267555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIgHDgIvXYJh0Vp2qLZ7H1LlAyo7y+I5muB1lb91hP2G18miKfSK6GvFR35OGh6onj7dmGz6L5QjZgVTzgl2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:45.268195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0154bd47b89b5d66c9ba595c11f8f36b5b233f61b7766bb849a795379b769ab4","sha256:3b1746968b8fd56e413f7abe9fd917196a1dac61682075d04c2cd3f48bbb4ab7"],"state_sha256":"c328e0f4da87f42cedc518e6fcd14a270f5602e47cce91dcc6a2e0a6494633df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ygI8nJqq8ESN5aesBCbXF3UxmZoHJsuSMEgS5XfSjABtizuvHLmRzfB5INmVau3qVYI37DxeE7AbYtAzsfyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:39:47.009495Z","bundle_sha256":"18f007e5e950d6c6db538b6ef8dd8e7f6d110cacec6976f920c0740ac17f8137"}}