{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SMGLDU7PEDZETAAML3E4DB2XG3","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":"e0bcc89e551d82419be31262f65ab22613ee9261dbbd98fabee668cfdfa01e09","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-30T13:49:18Z","title_canon_sha256":"4213fd49f67b7c2d7ba3185d3693f1e4820a33a2d1c8e179551f830528517b0e"},"schema_version":"1.0","source":{"id":"1007.5450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5450","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5450v1","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5450","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"SMGLDU7PEDZE","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SMGLDU7PEDZETAAM","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SMGLDU7P","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:2fe996e6d61d55cb8dcf703274ad35b9ad50155fae3a5e7f7353bb1551987564","target":"graph","created_at":"2026-05-18T04:42:45Z","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 obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2-\\epsilon)^{n}m^{O(1)} time, we show that for any e > 0; {\\sc Independent Set} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)} time, {\\sc Dominating Set} cannot be solved in (3-e)^{tw(G)}|V(G)|^{O(1)} time, {\\sc Max Cut} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)} time, {\\sc Odd Cycle Transversal} cannot be solved in (3-e)^{tw(G)}","authors_text":"Daniel Lokshtanov, D\\'aniel Marx, Saket Saurabh","cross_cats":["cs.CC","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-30T13:49:18Z","title":"Known Algorithms on Graphs of Bounded Treewidth are Probably Optimal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5450","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":"sha256:57cf7b2104c2da0d0cfcc8d9b5bb75358c082e475caff65c9aa6eee1ab810340","target":"record","created_at":"2026-05-18T04:42:45Z","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":"e0bcc89e551d82419be31262f65ab22613ee9261dbbd98fabee668cfdfa01e09","cross_cats_sorted":["cs.CC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-07-30T13:49:18Z","title_canon_sha256":"4213fd49f67b7c2d7ba3185d3693f1e4820a33a2d1c8e179551f830528517b0e"},"schema_version":"1.0","source":{"id":"1007.5450","kind":"arxiv","version":1}},"canonical_sha256":"930cb1d3ef20f249800c5ec9c1875736ec059859f464a9244132f5d6950dc815","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"930cb1d3ef20f249800c5ec9c1875736ec059859f464a9244132f5d6950dc815","first_computed_at":"2026-05-18T04:42:45.200094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:45.200094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FBdYyIe15LHRI/Pym8tuMwbNvMY5OHxulcH13RWA9rxNnXgjjoKd463Kle86VjeVsrqu5KyrZ0kNiWgMcuqcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:45.200687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57cf7b2104c2da0d0cfcc8d9b5bb75358c082e475caff65c9aa6eee1ab810340","sha256:2fe996e6d61d55cb8dcf703274ad35b9ad50155fae3a5e7f7353bb1551987564"],"state_sha256":"c167fe436d75202abb8914c1a8508729223797d725b57435c0d46ea919f45d21"}