{"paper":{"title":"Fast and Practical Single-Exponential Algorithms for Branchwidth","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"New algorithms compute the branchwidth of hypergraphs in O*(4^n) time and graphs in O(3.293^n) time.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hisao Tamaki, Taiki Kaneda, Yasuaki Kobayashi","submitted_at":"2026-05-17T11:28:40Z","abstract_excerpt":"In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is based on a conceptually simple recurrence on vertex sets and computes the branchwidth of an $n$-vertex hypergraph in time $\\mathcal{O}^*(4^n)$. This is the first single-exponential time algorithm for hypergraphs.\n  We have two algorithms tailored specifically for graphs. The first algorithm runs in time $\\mathcal{O}(3.293^n)$, improving upon the previously bes"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The basic algorithm computes the branchwidth of an n-vertex hypergraph in O*(4^n) time; this is the first single-exponential time algorithm for hypergraphs. The first graph algorithm runs in O(3.293^n) time, improving the previous O(3.4652^n) bound.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The recurrence relations correctly compute branchwidth when evaluated over all subsets (or a suitable subset family) of vertices; the paper assumes the standard definition of branchwidth via separations and that the dynamic-programming table entries can be combined without additional hidden costs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Presents the first single-exponential algorithm for hypergraph branchwidth at O*(4^n) and an improved O(3.293^n) algorithm for graphs that also outperforms prior practical implementations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"New algorithms compute the branchwidth of hypergraphs in O*(4^n) time and graphs in O(3.293^n) time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e1beb5d2ba320751e4d0255c954089196649231071ea790cfb31fe3de7b89dcc"},"source":{"id":"2605.17396","kind":"arxiv","version":1},"verdict":{"id":"8c5715e0-09e5-4497-b6f7-7bf95926c492","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:00:42.074260Z","strongest_claim":"The basic algorithm computes the branchwidth of an n-vertex hypergraph in O*(4^n) time; this is the first single-exponential time algorithm for hypergraphs. The first graph algorithm runs in O(3.293^n) time, improving the previous O(3.4652^n) bound.","one_line_summary":"Presents the first single-exponential algorithm for hypergraph branchwidth at O*(4^n) and an improved O(3.293^n) algorithm for graphs that also outperforms prior practical implementations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The recurrence relations correctly compute branchwidth when evaluated over all subsets (or a suitable subset family) of vertices; the paper assumes the standard definition of branchwidth via separations and that the dynamic-programming table entries can be combined without additional hidden costs.","pith_extraction_headline":"New algorithms compute the branchwidth of hypergraphs in O*(4^n) time and graphs in O(3.293^n) time."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17396/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:19.988097Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:12:51.348383Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.757820Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.699612Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f9bfe03d6532979b9b3a8a56cefea92ae95f8aaed9437107f9dbc3453db23b1e"},"references":{"count":28,"sample":[{"doi":"","year":2020,"title":"CoRR , volume =","work_id":"1cd79799-ee0b-48cb-ab71-52a1a9a95b3c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"2019 , doi =","work_id":"d8b238c0-7ead-4e1f-a278-bc95ec123527","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Computing rank-width exactly , journal =","work_id":"76eb9f99-296c-422e-9a97-317cd6496e6e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Fedor V. Fomin and Fr. Computing branchwidth via efficient triangulations and blocks , journal =. 2009 , doi =","work_id":"a658c3e9-80e5-4877-b48f-b8fdbecf4bbf","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Hicks , title =","work_id":"bb2f8693-9455-4c0f-b860-30249a9cbdfc","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"70b06c5c4049bcbcdee4c489e3eaa42541509124ea2e31db339b2f0b655b5e80","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"04c09a9edbf0f93e24fd661a9a414d83838c2e7c725d04aa4341d4ba33d955b8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}