{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LMJZIC46BMCWFKH47ENEETWSZO","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":"07af33d1d6e73f5cb72fe4697226d9ccfb1ae61f837bfdb06b872b2168a50c44","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-03-09T14:01:46Z","title_canon_sha256":"efb490e953a256be609b09eed664f5ac4d2ce3f369713ee48e67dc4637f1830c"},"schema_version":"1.0","source":{"id":"1803.03514","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03514","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03514v2","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03514","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"LMJZIC46BMCW","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LMJZIC46BMCWFKH4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LMJZIC46","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:fb2280b28c99b22f4969340e1e777d851dfdc8e04df63dfbceaa0e4dc5145e18","target":"graph","created_at":"2026-05-18T00:10:59Z","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 generalize the family of $(\\sigma, \\rho)$-problems and locally checkable vertex partition problems to their distance versions, which naturally captures well-known problems such as distance-$r$ dominating set and distance-$r$ independent set. We show that these distance problems are XP parameterized by the structural parameter mim-width, and hence polynomial on graph classes where mim-width is bounded and quickly computable, such as $k$-trapezoid graphs, Dilworth $k$-graphs, (circular) permutation graphs, interval graphs and their complements, convex graphs and their complements, $k$-polygon","authors_text":"Jan Arne Telle, Lars Jaffke, O-joung Kwon, Torstein J. F. Str{\\o}mme","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-03-09T14:01:46Z","title":"Generalized distance domination problems and their complexity on graphs of bounded mim-width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03514","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":"sha256:33d83b2e2f65b165c6d8bc3f79ef67ca691f6197df99ca6367dc451ce8803213","target":"record","created_at":"2026-05-18T00:10:59Z","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":"07af33d1d6e73f5cb72fe4697226d9ccfb1ae61f837bfdb06b872b2168a50c44","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-03-09T14:01:46Z","title_canon_sha256":"efb490e953a256be609b09eed664f5ac4d2ce3f369713ee48e67dc4637f1830c"},"schema_version":"1.0","source":{"id":"1803.03514","kind":"arxiv","version":2}},"canonical_sha256":"5b13940b9e0b0562a8fcf91a424ed2cb9b5953c8d546dd0efc7573426c6bfb84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b13940b9e0b0562a8fcf91a424ed2cb9b5953c8d546dd0efc7573426c6bfb84","first_computed_at":"2026-05-18T00:10:59.882356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:59.882356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5KeRpHXxKan5h/BlzGUH1DB2R6nOZlCE/BeuuNO+UNDMl9BsXJZJHRbSlxsM4dccZgLI5jg/SkbzN3EIVrPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:59.883107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03514","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33d83b2e2f65b165c6d8bc3f79ef67ca691f6197df99ca6367dc451ce8803213","sha256:fb2280b28c99b22f4969340e1e777d851dfdc8e04df63dfbceaa0e4dc5145e18"],"state_sha256":"b4b4debcc23d43536563f4bfa9fce5136942bc046b2d95cd181ed730300e5ed8"}