Pith Number

pith:CUJVGCLQ

pith:2026:CUJVGCLQMMSGRZGC76GPKUKDGW

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A dynamic $(1+\varepsilon)$-spanner for disk intersection graphs

Eva Rotenberg, Ivor van der Hoog, Johanne M. Vistisen, Sampson Wong, Sarita de Berg

Persistent data structures maintain a (1+ε)-spanner for dynamic disk intersection graphs with bounded diameters.

arxiv:2604.25397 v1 · 2026-04-28 · cs.CG · cs.DS

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

We maintain a (1+ε)-spanner over the disk intersection graph of a dynamic set of disks with diameters in [4, Ψ]. The spanner has size O(n ε^{-2} log Ψ log(ε^{-1})), uses O(ε^{-2} n log^4 n log Ψ) space, and supports updates in O((Ψ/ε)^2 log^4 n log^2 Ψ log^2(ε^{-1})) expected amortized time. For constant ε and Ψ the bounds become near-linear size, near-linear space, and polylogarithmic updates. The same spanner supports connectivity queries.

C2weakest assumption

All disks have diameters restricted to the fixed known interval [4, Ψ]; without this bounded-diameter assumption the size and update bounds no longer hold and the persistent-structure approach may not apply directly.

C3one line summary

A dynamic (1+ε)-spanner of size O(n ε^{-2} log Ψ log(ε^{-1})) with O((Ψ/ε)^2 log^4 n log^2 Ψ log^2(ε^{-1})) expected amortized update time for disk intersection graphs with bounded diameters.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] Geometric spanners for points inside a polygonal domain 2015 · doi:10.4230/lipics.socg.2015.186

[2] 4 Ingo Althöfer, Gautam Das, David P 1998 · doi:10.1109/sfcs.1998.743504

[3] 5 Shinwoo An, Eunjin Oh, and Jie Xue 2025 · doi:10.1007/bf02189308

[4] 34 A dynamic(1 +ε)-spanner for disk intersection graphs 21 Timothy M · doi:10.1137/19m1246493

[5] doi:10.4230/LIPIcs.SoCG.2023.23 2023 · doi:10.4230/lipics.socg.2023.23

Receipt and verification

First computed	2026-05-20T00:00:39.478666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1513530970632468e4c2ff8cf5514335aabce3ce302d0ac1dc572f12cfb4001e

Aliases

arxiv: 2604.25397 · arxiv_version: 2604.25397v1 · doi: 10.48550/arxiv.2604.25397 · pith_short_12: CUJVGCLQMMSG · pith_short_16: CUJVGCLQMMSGRZGC · pith_short_8: CUJVGCLQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CUJVGCLQMMSGRZGC76GPKUKDGW \
  | 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: 1513530970632468e4c2ff8cf5514335aabce3ce302d0ac1dc572f12cfb4001e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "443f7d519b2f2ae5343e757fd1c45ee26c253a54a4c7631ef644a95efa52f1f3",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-04-28T09:07:25Z",
    "title_canon_sha256": "f5df67445dee46faef61c3c755fba7e8b52f71261903e5d8a076c96b6148a4fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25397",
    "kind": "arxiv",
    "version": 1
  }
}