{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J57TBK4KCEV23HUTXJ7XRDDB6M","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":"353c7c15b5826c75c15710fd7763407d9d8a0fc4e5cefe76cbc231f473b4d037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-10-19T15:51:38Z","title_canon_sha256":"e2bb47b8912e83dcebb2906323014bf7c905bbad394b85d84333d5e81630373d"},"schema_version":"1.0","source":{"id":"1110.4319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4319","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4319v2","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4319","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"J57TBK4KCEV2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J57TBK4KCEV23HUT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J57TBK4K","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:62ec0f724866960b9cda824aac6000a3ac73757bdf7b58614800fa869f664e29","target":"graph","created_at":"2026-05-18T04:10:36Z","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 graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the k parts need to be of equal-size, and where they must separate a set of k given terminals. We consider a common generalization of these two problems, and design for it an $O(\\sqrt{\\log n\\log k})$-approximation algorithm. This improves over an $O(\\log^2 n)$ approximation for the second version, and roughly $O(k\\log n)$ approxima","authors_text":"Joseph (Seffi) Naor, Konstantin Makarychev, Nikhil Bansal, Robert Krauthgamer, Roy Schwartz, Uriel Feige, Viswanath Nagarajan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-10-19T15:51:38Z","title":"Min-Max Graph Partitioning and Small Set Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4319","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:a5eb924c14ad67d0cc29c9154c83484fa5bb5baa92724621947fe7c5128f6d44","target":"record","created_at":"2026-05-18T04:10:36Z","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":"353c7c15b5826c75c15710fd7763407d9d8a0fc4e5cefe76cbc231f473b4d037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-10-19T15:51:38Z","title_canon_sha256":"e2bb47b8912e83dcebb2906323014bf7c905bbad394b85d84333d5e81630373d"},"schema_version":"1.0","source":{"id":"1110.4319","kind":"arxiv","version":2}},"canonical_sha256":"4f7f30ab8a112bad9e93ba7f788c61f30d20fcfa14d1a9aec69829bd6fc07e4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f7f30ab8a112bad9e93ba7f788c61f30d20fcfa14d1a9aec69829bd6fc07e4a","first_computed_at":"2026-05-18T04:10:36.833738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:36.833738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWz8kHwTRXiTaDpNVXY/109rfE+mTk6poVKGd3Y7gN0Z9BP7rfgx+wvwKKak6290NaWJ05v6Q9jKxjaGFChoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:36.834462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5eb924c14ad67d0cc29c9154c83484fa5bb5baa92724621947fe7c5128f6d44","sha256:62ec0f724866960b9cda824aac6000a3ac73757bdf7b58614800fa869f664e29"],"state_sha256":"a9d473717eed8932ba7cb3e8bfa008512880d3f401177a34fc78dbba6cdd409a"}