Pith Number

pith:SNWO7HP3

pith:2026:SNWO7HP3WNG5BF7OXKGNLGDY5C

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Achieving $\alpha$-Fairness in Clustered Cell-Free Networking: A Tight Relaxation Approach

Boxiang Ren, Chaowen Deng, Hao Wu, Jie Fan, Jingchen Peng, Junyuan Wang, Ziyuan Lyu

Reformulating the clustering problem as a continuous optimization establishes exact equivalence to the integer program for alpha-fairness across four cases.

arxiv:2605.16960 v1 · 2026-05-16 · cs.IT · math.IT

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For each case, we establish the exact equivalence between the original integer program and its continuous relaxation, and develop efficient algorithms with guaranteed convergence.

C2weakest assumption

The closed-form deterministic equivalent of the ergodic sum capacity remains accurate enough after the clustering decisions are made that the reformulated continuous problem yields solutions whose true performance matches the claimed fairness and rate gains.

C3one line summary

A unified alpha-fairness scheme for clustered cell-free networking is achieved via closed-form deterministic equivalents and tight continuous relaxations that are exactly equivalent to the integer program in four cases of alpha.

References

51 extracted · 51 resolved · 0 Pith anchors

[1] Towards load- balanced clustered cell-free networking: A tight relaxation approach, 2025

[2] A vision of 6G wireless systems: Applications, trends, technologies, and open research problems, 2020

[3] Cell edge performance of cellular mobile systems, 2011

[4] D. Tse and P. Viswanath,Fundamentals of Wireless Communication. United States of America by Cambridge University Press, New York, 2005 2005

[5] Shannon-theoretic approach to a Gaussian cellular multiple- access channel, 1994

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:33.001067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

936cef9dfbb34dd097eeba8cd59878e8a5ac89d56987f1f063f254e0a244aed9

Aliases

arxiv: 2605.16960 · arxiv_version: 2605.16960v1 · doi: 10.48550/arxiv.2605.16960 · pith_short_12: SNWO7HP3WNG5 · pith_short_16: SNWO7HP3WNG5BF7O · pith_short_8: SNWO7HP3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SNWO7HP3WNG5BF7OXKGNLGDY5C \
  | 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: 936cef9dfbb34dd097eeba8cd59878e8a5ac89d56987f1f063f254e0a244aed9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64ad16c68143587f02ab852914247f89c2d6df2b390f9cfdc8e56a7f88d7c3b3",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-16T12:23:04Z",
    "title_canon_sha256": "695923478310d2d6a7dc9af30e921d8d06da8f6439c17514c092715d46680248"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16960",
    "kind": "arxiv",
    "version": 1
  }
}