{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JDG7JKFUAMHX2UH33B37AAMG7I","short_pith_number":"pith:JDG7JKFU","schema_version":"1.0","canonical_sha256":"48cdf4a8b4030f7d50fbd877f00186fa368cc50d1b88d442403b0ae25601deb7","source":{"kind":"arxiv","id":"1303.1786","version":2},"attestation_state":"computed","paper":{"title":"Meta-Kernelization with Structural Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DS","authors_text":"Friedrich Slivovsky, Robert Ganian, Stefan Szeider","submitted_at":"2013-03-07T19:24:06Z","abstract_excerpt":"Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al. (FOCS'10), apply to optimization problems parameterized by solution size. We present the first meta-kernelization theorems that use a structural parameters of the input and not the solution size. Let C be a graph class. We define the C-cover number of a graph to be a the smallest number of modules the vertex set can be partitioned into, such that each modul"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.1786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-03-07T19:24:06Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"ac5caccf3693e626a0767b68187d5b04df5d8ec5733a895213275f55ec1df523","abstract_canon_sha256":"9a514a30c9abfc0c040f78f7237c88d8c3f73566c0ee4bfbb3e63d641dec78f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:34.054916Z","signature_b64":"X/SwLQbfrq9uKFyJYJk0soEPRbts075nowhCgeOMJgpt7/s+CSCoxf2O931Ct2WlY8UlpywibB/nw4PIQa1KDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48cdf4a8b4030f7d50fbd877f00186fa368cc50d1b88d442403b0ae25601deb7","last_reissued_at":"2026-05-18T03:27:34.054336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:34.054336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Meta-Kernelization with Structural Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DS","authors_text":"Friedrich Slivovsky, Robert Ganian, Stefan Szeider","submitted_at":"2013-03-07T19:24:06Z","abstract_excerpt":"Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al. (FOCS'10), apply to optimization problems parameterized by solution size. We present the first meta-kernelization theorems that use a structural parameters of the input and not the solution size. Let C be a graph class. We define the C-cover number of a graph to be a the smallest number of modules the vertex set can be partitioned into, such that each modul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1786","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.1786","created_at":"2026-05-18T03:27:34.054405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1786v2","created_at":"2026-05-18T03:27:34.054405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1786","created_at":"2026-05-18T03:27:34.054405+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDG7JKFUAMHX","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDG7JKFUAMHX2UH3","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDG7JKFU","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I","json":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I.json","graph_json":"https://pith.science/api/pith-number/JDG7JKFUAMHX2UH33B37AAMG7I/graph.json","events_json":"https://pith.science/api/pith-number/JDG7JKFUAMHX2UH33B37AAMG7I/events.json","paper":"https://pith.science/paper/JDG7JKFU"},"agent_actions":{"view_html":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I","download_json":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I.json","view_paper":"https://pith.science/paper/JDG7JKFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1786&json=true","fetch_graph":"https://pith.science/api/pith-number/JDG7JKFUAMHX2UH33B37AAMG7I/graph.json","fetch_events":"https://pith.science/api/pith-number/JDG7JKFUAMHX2UH33B37AAMG7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I/action/storage_attestation","attest_author":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I/action/author_attestation","sign_citation":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I/action/citation_signature","submit_replication":"https://pith.science/pith/JDG7JKFUAMHX2UH33B37AAMG7I/action/replication_record"}},"created_at":"2026-05-18T03:27:34.054405+00:00","updated_at":"2026-05-18T03:27:34.054405+00:00"}