{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MTOUR5OVZFHUSC3SDSEQQHNGF4","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":"fed083c2d7a2fde067c4634e0a40a4a61c9ffc889f012a748cee92460df0fec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-10-05T09:37:46Z","title_canon_sha256":"a5a036ce81463113cd6df79828358c8a076529136716680d41cff26bcfb364f0"},"schema_version":"1.0","source":{"id":"2210.02117","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.02117","created_at":"2026-07-05T05:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"2210.02117v2","created_at":"2026-07-05T05:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.02117","created_at":"2026-07-05T05:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"MTOUR5OVZFHU","created_at":"2026-07-05T05:23:33Z"},{"alias_kind":"pith_short_16","alias_value":"MTOUR5OVZFHUSC3S","created_at":"2026-07-05T05:23:33Z"},{"alias_kind":"pith_short_8","alias_value":"MTOUR5OV","created_at":"2026-07-05T05:23:33Z"}],"graph_snapshots":[{"event_id":"sha256:c396733700b4c48d23eb4b89346d48d4dc575cdc9a4edd674537eed998cba0cf","target":"graph","created_at":"2026-07-05T05:23:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.02117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the $2^{O(k^2)} n^{O(1)}$ time algorithm given by Bui-Xuan, Telle, and Vatshelle [Discret. Appl. Math., 2010] and it answers the open question of Bergougnoux and Kant\\'{e} [SIAM J. Discret. Math., 2021]. We also show that the known $2^{O(k^2)} n^{O(1)}$ time algorithms for Weighted Dominating Set, Maximum Induced Matching and Feedback Vertex Set parameterized by rank-width $k$ are optimal assuming","authors_text":"Benjamin Bergougnoux, Jesper Nederlof, Tuukka Korhonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-10-05T09:37:46Z","title":"Tight Lower Bounds for Problems Parameterized by Rank-width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.02117","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":"sha256:6516a32a158389fdf28943521e5ac24b82fecee215eb93f4d8d775529d3fded6","target":"record","created_at":"2026-07-05T05:23:33Z","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":"fed083c2d7a2fde067c4634e0a40a4a61c9ffc889f012a748cee92460df0fec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-10-05T09:37:46Z","title_canon_sha256":"a5a036ce81463113cd6df79828358c8a076529136716680d41cff26bcfb364f0"},"schema_version":"1.0","source":{"id":"2210.02117","kind":"arxiv","version":2}},"canonical_sha256":"64dd48f5d5c94f490b721c89081da62f050d408b388f2653d62009d1941212e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64dd48f5d5c94f490b721c89081da62f050d408b388f2653d62009d1941212e4","first_computed_at":"2026-07-05T05:23:33.661891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:23:33.661891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+ewONETGGaDV3tEtVwfStczvMQqJ4Ba/kBKMBiYNe7T/LsQLhAfcscHQB4tErCQv4MV3EFARepS4Uyh18daCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:23:33.662308Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.02117","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6516a32a158389fdf28943521e5ac24b82fecee215eb93f4d8d775529d3fded6","sha256:c396733700b4c48d23eb4b89346d48d4dc575cdc9a4edd674537eed998cba0cf"],"state_sha256":"2a8c88e0e54ecf197874e050e115cdbad4d957db4d91aff0d7006fc9b8b26fa9"}