{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:HTYAFHIMOKVCEXW6RXCXPSXQH6","short_pith_number":"pith:HTYAFHIM","schema_version":"1.0","canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","source":{"kind":"arxiv","id":"2206.11832","version":6},"attestation_state":"computed","paper":{"title":"On the parameterized complexity of computing tree-partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Carla Groenland, Hans L. Bodlaender, Hugo Jacob","submitted_at":"2022-06-23T16:59:40Z","abstract_excerpt":"We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, constructs a tree-partition of width $O(k^7)$ for $G$ or reports that $G$ has tree-partition-width more than $k$, in time $k^{O(1)}n^2$. We can improve slightly on the approximation factor by sacrificing the dependence on $k$, or on $n$. On the other hand, we show the p"},"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":"2206.11832","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-06-23T16:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"0ca96f85170f72a941c975dacbc5fb3e9936e95be3a39a25cd0e71b596033d72","abstract_canon_sha256":"4a95920d804c2bb95b9f3320353787aeeb15d15213bba10b7a55e52a4231a142"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:04.830553Z","signature_b64":"ph8bTbAKYTHZkvQGUtRzfqonQBUHOzp38qebeorohAGv4QJ67RDPToGy6KK2zemVZY0cu9TI3nNjgtObCDkPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cf0029d0c72aa225ede8dc577caf03f83fd4852e7b5d79fa0a338a05cb856a1","last_reissued_at":"2026-07-05T10:16:04.830112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:04.830112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the parameterized complexity of computing tree-partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Carla Groenland, Hans L. Bodlaender, Hugo Jacob","submitted_at":"2022-06-23T16:59:40Z","abstract_excerpt":"We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, constructs a tree-partition of width $O(k^7)$ for $G$ or reports that $G$ has tree-partition-width more than $k$, in time $k^{O(1)}n^2$. We can improve slightly on the approximation factor by sacrificing the dependence on $k$, or on $n$. On the other hand, we show the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11832","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.11832/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2206.11832","created_at":"2026-07-05T10:16:04.830171+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.11832v6","created_at":"2026-07-05T10:16:04.830171+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11832","created_at":"2026-07-05T10:16:04.830171+00:00"},{"alias_kind":"pith_short_12","alias_value":"HTYAFHIMOKVC","created_at":"2026-07-05T10:16:04.830171+00:00"},{"alias_kind":"pith_short_16","alias_value":"HTYAFHIMOKVCEXW6","created_at":"2026-07-05T10:16:04.830171+00:00"},{"alias_kind":"pith_short_8","alias_value":"HTYAFHIM","created_at":"2026-07-05T10:16:04.830171+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.18923","citing_title":"Graph-Based Operator Learning from Limited Data on Irregular Domains","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6","json":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6.json","graph_json":"https://pith.science/api/pith-number/HTYAFHIMOKVCEXW6RXCXPSXQH6/graph.json","events_json":"https://pith.science/api/pith-number/HTYAFHIMOKVCEXW6RXCXPSXQH6/events.json","paper":"https://pith.science/paper/HTYAFHIM"},"agent_actions":{"view_html":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6","download_json":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6.json","view_paper":"https://pith.science/paper/HTYAFHIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.11832&json=true","fetch_graph":"https://pith.science/api/pith-number/HTYAFHIMOKVCEXW6RXCXPSXQH6/graph.json","fetch_events":"https://pith.science/api/pith-number/HTYAFHIMOKVCEXW6RXCXPSXQH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/action/storage_attestation","attest_author":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/action/author_attestation","sign_citation":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/action/citation_signature","submit_replication":"https://pith.science/pith/HTYAFHIMOKVCEXW6RXCXPSXQH6/action/replication_record"}},"created_at":"2026-07-05T10:16:04.830171+00:00","updated_at":"2026-07-05T10:16:04.830171+00:00"}