Pith Number

pith:FM357X3Y

pith:2026:FM357X3Y27GLF3OVCSIPTU2AUP

not attested not anchored not stored refs resolved

Fast and effective algorithms for fair clustering at scale

Claudio Mantuano, Manuel Kammermann, Philipp Baumann

Heuristics achieve scalable fair k-means clustering by enforcing group representation targets while minimizing sum of squared distances.

arxiv:2605.13759 v1 · 2026-05-13 · cs.LG

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\usepackage{pith}
\pithnumber{FM357X3Y27GLF3OVCSIPTU2AUP}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

The proposed heuristics outperform existing approaches in comprehensive numerical experiments on benchmark datasets while providing precise control over the cost-fairness trade-off and scaling to instances with millions of objects in seconds.

C2weakest assumption

That the fairness constraint (each protected group sufficiently represented in each cluster) can be satisfied without destroying the geometric structure that makes the clustering cost meaningful, and that the heuristics' local-search or relaxation steps do not systematically miss globally better trade-off points.

C3one line summary

A framework plus three heuristics for fair clustering that give precise cost-fairness control and scale to millions of objects while beating existing solvers on benchmark data.

References

57 extracted · 57 resolved · 2 Pith anchors

[1] Applied Soft Computing , volume= 2010

[2] Journal of the Operational Research Society , volume= 2020

[3] Socio-Economic Planning Sciences , volume= 2021

[4] Expert Systems with Applications , volume= 2023

[5] Journal of Mathematics , volume= 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:16.315543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b37dfdf78d7ccb2edd51490f9d340a3f2a1703e95610df76e3598b1e5c96bdd

Aliases

arxiv: 2605.13759 · arxiv_version: 2605.13759v1 · doi: 10.48550/arxiv.2605.13759 · pith_short_12: FM357X3Y27GL · pith_short_16: FM357X3Y27GLF3OV · pith_short_8: FM357X3Y

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FM357X3Y27GLF3OVCSIPTU2AUP \
  | 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: 2b37dfdf78d7ccb2edd51490f9d340a3f2a1703e95610df76e3598b1e5c96bdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce06f52bbc636af12e1b1db2fb071b33b4e5d5e0fb3676149fa97eb574a8cf59",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T16:40:07Z",
    "title_canon_sha256": "9a4035c1b87daa282fe8038589c6d44ea5cf048d0a83a4574d0280933eeaa728"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13759",
    "kind": "arxiv",
    "version": 1
  }
}