Pith Number

pith:N6GU4YCX

pith:2026:N6GU4YCX3RAQ56FBKSRTZXLY73

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Distributed Approximate Maximum Matching and Minimum Vertex Cover via Generalized Graph Decomposition

Peter Davies-Peck

Randomized algorithms achieve 2+ε-approximate maximum matching and approximate weighted minimum vertex cover in O(log n / log² log n) rounds in the LOCAL model.

arxiv:2605.13264 v1 · 2026-05-13 · cs.DS

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Claims

C1strongest claim

We show randomized algorithms for 2+ε-approximate maximum matching and approximate (weighted) minimum vertex cover taking O(log n / log² log n) rounds.

C2weakest assumption

The novel graph decomposition generalizing Miller, Peng and Xu works as claimed to reduce the effective degree of high-degree graphs in the LOCAL model.

C3one line summary

Randomized LOCAL-model algorithms achieve 2+ε-approximate maximum matching and approximate minimum vertex cover in O(log n / log² log n) rounds via a generalized graph decomposition, establishing that n-dependent complexity is required.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] B. Awerbuch, M. Luby, A.V. Goldberg, and S.A. Plotkin. Network decomposition and locality in distributed computation. In30th Annual Symposium on Foundations of Computer Science, pages 364– 369, 1989 1989

[2] Massively parallel minimum spanning tree in general metric spaces 2025

[3] Distributed approximation of maximum independent set and maximum matching 2017

[4] A distributed(2 +ε)- approximation for vertex cover inO(log ∆/εlog log ∆)rounds.J 2017

[5] The locality of distributed symmetry breaking 2016

Receipt and verification

First computed	2026-05-18T02:44:49.327891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f8d4e6057dc410ef8a154a33cdd78fec0d56b159e69a643ef0e6dae34a4d73c

Aliases

arxiv: 2605.13264 · arxiv_version: 2605.13264v1 · doi: 10.48550/arxiv.2605.13264 · pith_short_12: N6GU4YCX3RAQ · pith_short_16: N6GU4YCX3RAQ56FB · pith_short_8: N6GU4YCX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N6GU4YCX3RAQ56FBKSRTZXLY73 \
  | 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: 6f8d4e6057dc410ef8a154a33cdd78fec0d56b159e69a643ef0e6dae34a4d73c

Canonical record JSON

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    "abstract_canon_sha256": "89893655d03c07aab82e493ed435ec0132af8e91be3b7db8b3482b23b997ce8c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T09:45:29Z",
    "title_canon_sha256": "747c6329186ea98414002dbbc467e4de09f1f5f2f37dd0c1f9e5365be78953b6"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}