Pith Number

pith:SEPTWRD2

pith:2026:SEPTWRD2N3OSFRVETIJW6MDVT5

not attested not anchored not stored refs resolved

Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm

Anders Bjorholm Dahl, Christian M{\o}ller Mikkelstrup, Inge Li G{\o}rtz, Philip Bille, Vedrana Andersen Dahl

The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices.

arxiv:2605.13402 v1 · 2026-05-13 · cs.CV · cs.DS

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\pithnumber{SEPTWRD2N3OSFRVETIJW6MDVT5}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of O(m|C|), where m and |C| are the number of edges and the capacity of the cut, respectively.

C2weakest assumption

The compact graph representation preserves the correctness of the minimum-cut computation and incurs no hidden asymptotic overhead on the claimed time bound.

C3one line summary

The fcBK algorithm computes minimum s-t cuts in O(m|C|) time and supports graphs with up to 10^9 vertices using a compact representation.

References

60 extracted · 60 resolved · 0 Pith anchors

[1] An experimental comparison of min- cut/max-flow algorithms for energy minimization in vision, 2004

[2] Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images, 2001

[3] Efficiently solving dynamic markov random fields using graph cuts, 2005

[4] Graph cuts and efficient n-d image segmentation, 2006

[5] Fast approximate energy minimization with label costs, 2012

Receipt and verification

First computed	2026-05-18T02:44:47.581611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae

Aliases

arxiv: 2605.13402 · arxiv_version: 2605.13402v1 · doi: 10.48550/arxiv.2605.13402 · pith_short_12: SEPTWRD2N3OS · pith_short_16: SEPTWRD2N3OSFRVE · pith_short_8: SEPTWRD2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5 \
  | 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: 911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54db0d31b1f55f59b9df307be7c8d02f54d28d13ec662aa73933e849fde5fae8",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-13T11:57:35Z",
    "title_canon_sha256": "9a100120b5d9f29eaeb9d42f5fb38e41f00b3b219b4b3910a995deae3864c268"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13402",
    "kind": "arxiv",
    "version": 1
  }
}