{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7BRDXHWLZEG5PFVII64QSPW2N5","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":"0aff6c644937b46767b1670e0fabbaae8cf36fc32806c33a4d3107a86f3258c4","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:45:59Z","title_canon_sha256":"7e50b7dc08fe0514645fdd3e431f2686830e2ad6d9b015200933eb2dd1cb99d3"},"schema_version":"1.0","source":{"id":"1309.6850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6850","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6850v1","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6850","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"7BRDXHWLZEG5","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7BRDXHWLZEG5PFVI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7BRDXHWL","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:eef13fd2fcbe7725097559affdb98159b4cd14ff7c8f4f1aa99c7b77ea2a3493","target":"graph","created_at":"2026-05-18T03:12:10Z","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":"A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constraints can be solved much more efficiently than general submodular optimization methods by a reduction to a maximum flow problem. Furthermore, we give some applications, including sparse optimization methods, in which the proposed methods are effective. Additionally, we evaluate t","authors_text":"Kiyohito Nagano, Yoshinobu Kawahara","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:45:59Z","title":"Structured Convex Optimization under Submodular Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6850","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":"sha256:99e819b8f38008ba711756eac6b1391d272add21aa6f135d2cb4715d5122178d","target":"record","created_at":"2026-05-18T03:12:10Z","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":"0aff6c644937b46767b1670e0fabbaae8cf36fc32806c33a4d3107a86f3258c4","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-09-26T12:45:59Z","title_canon_sha256":"7e50b7dc08fe0514645fdd3e431f2686830e2ad6d9b015200933eb2dd1cb99d3"},"schema_version":"1.0","source":{"id":"1309.6850","kind":"arxiv","version":1}},"canonical_sha256":"f8623b9ecbc90dd796a847b9093eda6f5e16185803fb5c8c97eea43c5056c308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8623b9ecbc90dd796a847b9093eda6f5e16185803fb5c8c97eea43c5056c308","first_computed_at":"2026-05-18T03:12:10.083473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:10.083473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8OrCh3aRFXou9NP+1eaJi4P8xPtJX2OanMol+Y6qM1pH34/UdmS+Pca6L7RIaa/6nzYQAy7CmrbeW13Jl1NTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:10.084079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99e819b8f38008ba711756eac6b1391d272add21aa6f135d2cb4715d5122178d","sha256:eef13fd2fcbe7725097559affdb98159b4cd14ff7c8f4f1aa99c7b77ea2a3493"],"state_sha256":"5e22495725eba651a9bfb1a09a9728aa2d4ebf6cd92de7071a252668018c977b"}