Pith Number

pith:2FYE7UUQ

pith:2026:2FYE7UUQGZGKCMT4QLZS2B53AY

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Fast and Practical Single-Exponential Algorithms for Branchwidth

Hisao Tamaki, Taiki Kaneda, Yasuaki Kobayashi

New algorithms compute the branchwidth of hypergraphs in O*(4^n) time and graphs in O(3.293^n) time.

arxiv:2605.17396 v1 · 2026-05-17 · cs.DS

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] CoRR , volume = 2020

[2] 2019 , doi = 2019

[3] Computing rank-width exactly , journal = 2009

[4] Fedor V. Fomin and Fr. Computing branchwidth via efficient triangulations and blocks , journal =. 2009 , doi = 2009

[5] Hicks , title = 2005

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:56.386924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1704fd290364ca1327c82f32d07bb060c886739efd2335069a7de2e7dd141fe

Aliases

arxiv: 2605.17396 · arxiv_version: 2605.17396v1 · doi: 10.48550/arxiv.2605.17396 · pith_short_12: 2FYE7UUQGZGK · pith_short_16: 2FYE7UUQGZGKCMT4 · pith_short_8: 2FYE7UUQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2FYE7UUQGZGKCMT4QLZS2B53AY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d1704fd290364ca1327c82f32d07bb060c886739efd2335069a7de2e7dd141fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b95e1425713c1304a58562434909354d68e8753a4996f5786b1022532d751cf3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-17T11:28:40Z",
    "title_canon_sha256": "8ed53f627ecf884699e69f907aba89440e4069a049436f3bccce901f4e756545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17396",
    "kind": "arxiv",
    "version": 1
  }
}