{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L4FTXUO2LVF75EB5VV7YKLDNXO","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":"7e490849e1dacb2c9f54a799f565a0cdb08aa87bf8dcc4133840d0b528091e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-11T20:21:32Z","title_canon_sha256":"f7835ffccbe3c23b6eb8ffb37737b42fab5fc1496814a8ed320eaa19d7d1cb01"},"schema_version":"1.0","source":{"id":"1311.2563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2563","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2563v2","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2563","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"L4FTXUO2LVF7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L4FTXUO2LVF75EB5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L4FTXUO2","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:6e586e3b277cdd1879ad3d15455fc2ef845f7e42d8f7fe136bbeaded158087bf","target":"graph","created_at":"2026-05-18T02:56:11Z","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":"In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| \\leq 1$ and there are at most $k$ edges with one endpoint in $A$ and the other in $B$. In this paper we give an algorithm for Minimum Bisection with running time $O(2^{O(k^{3})}n^3 \\log^3 n)$. This is the first fixed parameter tractable algorithm for Minimum Bisection. At the core of our algorithm lies a new decomposition theorem that states that every graph $G$ can be decomposed by small s","authors_text":"Daniel Lokshtanov, Marcin Pilipczuk, Marek Cygan, Micha{\\l} Pilipczuk, Saket Saurabh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-11T20:21:32Z","title":"Minimum Bisection is fixed parameter tractable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2563","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":"sha256:9578c3d7eedf79ddfe1dda69ad77b8b5b9834af7582a956f12ca22db359e9e41","target":"record","created_at":"2026-05-18T02:56:11Z","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":"7e490849e1dacb2c9f54a799f565a0cdb08aa87bf8dcc4133840d0b528091e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-11T20:21:32Z","title_canon_sha256":"f7835ffccbe3c23b6eb8ffb37737b42fab5fc1496814a8ed320eaa19d7d1cb01"},"schema_version":"1.0","source":{"id":"1311.2563","kind":"arxiv","version":2}},"canonical_sha256":"5f0b3bd1da5d4bfe903dad7f852c6dbb830987ab9b6427a26636301be91d860d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f0b3bd1da5d4bfe903dad7f852c6dbb830987ab9b6427a26636301be91d860d","first_computed_at":"2026-05-18T02:56:11.305979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:11.305979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZwV5arrOIBqBoBcgU7a3YePblEvfbCbjMI0JqQbHsDIVW7y4aCmA6azRB2v5rsHi7ESGitrXzux/CMiSnaNAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:11.306376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9578c3d7eedf79ddfe1dda69ad77b8b5b9834af7582a956f12ca22db359e9e41","sha256:6e586e3b277cdd1879ad3d15455fc2ef845f7e42d8f7fe136bbeaded158087bf"],"state_sha256":"3322493698cf8f47ada1f16ff0b576d19149c9ca91e5406346e765b429924331"}