{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YOMB6KJ6VXLZ2NFFMDX2RE2ZKC","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":"da7896262d4a2fea617578027764064445060e7d71f200a73bf0da8813fb8318","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-08-26T06:24:53Z","title_canon_sha256":"981bfe68b8387361c41ef1a861384777d4dd43537b18728cb2ddd76872edebab"},"schema_version":"1.0","source":{"id":"1108.5248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5248","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5248v2","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5248","created_at":"2026-05-18T02:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"YOMB6KJ6VXLZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YOMB6KJ6VXLZ2NFF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YOMB6KJ6","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:91aac4a03d978d0f4a3fbbc9cabc0b00e7c927d25ffe983665eddee4d01042b4","target":"graph","created_at":"2026-05-18T02:21:37Z","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":"Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation [14], which maintains knowledge about synergies between agents in the form of an edge weighted graph.\n  We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a","authors_text":"Morteza Zadimoghaddam, Pushmeet Kohli, Vladimir Kolmogorov, Yoram Bachrach","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-08-26T06:24:53Z","title":"Optimal Coalition Structures in Cooperative Graph Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5248","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:d1430e2f085136627e2762592d783e7cd5a7eb72defeaf0aa5c9afa17412f51b","target":"record","created_at":"2026-05-18T02:21:37Z","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":"da7896262d4a2fea617578027764064445060e7d71f200a73bf0da8813fb8318","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-08-26T06:24:53Z","title_canon_sha256":"981bfe68b8387361c41ef1a861384777d4dd43537b18728cb2ddd76872edebab"},"schema_version":"1.0","source":{"id":"1108.5248","kind":"arxiv","version":2}},"canonical_sha256":"c3981f293eadd79d34a560efa8935950be86ce3e834df69f90d045b9a6237a38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3981f293eadd79d34a560efa8935950be86ce3e834df69f90d045b9a6237a38","first_computed_at":"2026-05-18T02:21:37.054785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:37.054785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3fRUZG4apZyWmWgu9iJ/DYow53tM2Saen8T3npYusU6A1nLylEHBXF87yu8d9Buc/lcsGvDtKSFZ7of83sjSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:37.055302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1430e2f085136627e2762592d783e7cd5a7eb72defeaf0aa5c9afa17412f51b","sha256:91aac4a03d978d0f4a3fbbc9cabc0b00e7c927d25ffe983665eddee4d01042b4"],"state_sha256":"b1b25d0b762a16e8da066f6c77c4a97e573db5feef27bcb4ceb1faf59b783bd2"}