Pith Number

pith:W75YYP3D

pith:2026:W75YYP3D5WEIXFINR4PE7KQ4A3

not attested not anchored not stored refs resolved

Low-Cost Arborescence Under Edge Faults

Dipan Dey, Telikepalli Kavitha

A subgraph of size O(n^{3/2}) lets you recover a 2-approximate min-cost arborescence after any single edge fault.

arxiv:2605.13800 v1 · 2026-05-13 · cs.DS

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\usepackage{pith}
\pithnumber{W75YYP3D5WEIXFINR4PE7KQ4A3}

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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

We show a simple polynomial-time algorithm to construct a subgraph H of size O(n^{3/2}) such that, for any f in E, a min-cost arborescence in H-f is a 2-approximation of a min-cost arborescence in G-f.

C2weakest assumption

That a min-cost arborescence can be computed efficiently inside the constructed subgraph H-f and that the 2-approximation guarantee holds for the specific construction given in the full paper.

C3one line summary

An O(n^{3/2})-size subgraph preserves 2-approximate min-cost arborescences under single edge faults with fast updates, plus a tight k times rank bound for k-fault-tolerant matroid preservers.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Fault tolerant reachability for directed graphs 2015 · doi:10.1007/978-3-662-48653-5_35

[2] Fault-tolerant subgraph for single-source reachability: General and optimal.SIAM Journal on Computing, 47(1):80–95, 2018 2018

[3] 2 BLM12 Surender Baswana, Utkarsh Lath, and Anuradha S 2013 · doi:10.1007/s00453-012-9621-y

[4] Matthias Bentert, Fedor V . Fomin, Petr A. Golovach, and Laure Morelle. Fault-tolerant matroid bases. InProceedings of the 33rd Annual European Symposium on Algorithms, (ESA 2025), pages 83:1–83:14, 2025

[5] URL: https://doi.org/10.4230/LIPIcs.ESA.2025.83, doi:10.4230/LIPICS. ESA.2025.83 2025 · doi:10.4230/lipics.esa.2025.83

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:15.520131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7fb8c3f63ed888b950d8f1e4faa1c06e8d888ac1853ff90491090853ec6c4fc

Aliases

arxiv: 2605.13800 · arxiv_version: 2605.13800v1 · doi: 10.48550/arxiv.2605.13800 · pith_short_12: W75YYP3D5WEI · pith_short_16: W75YYP3D5WEIXFIN · pith_short_8: W75YYP3D

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/W75YYP3D5WEIXFINR4PE7KQ4A3 \
  | 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: b7fb8c3f63ed888b950d8f1e4faa1c06e8d888ac1853ff90491090853ec6c4fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dcf2122a77c137a3fc50a4afa07023e50ca64e77f3af95462baf4fa7227f0f7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T17:21:08Z",
    "title_canon_sha256": "f9143c328e381ae7c2a43530277598f9e84cfe255c167b3b2d159f86e5e44537"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13800",
    "kind": "arxiv",
    "version": 1
  }
}