Pith Number

pith:Y42FOHJD

pith:2026:Y42FOHJD636FNGP27W3L6ZPQI6

not attested not anchored not stored refs pending

Near-Linear Time Generalized Sinkhorn Algorithms for Bounded Genus Graphs

Ananya Parashar, Derek Long, Dwaipayan Saha, Krzysztof Choromanski

GenusSink delivers near-linear time approximate Sinkhorn algorithms for bounded-genus graphs with shortest-path costs.

arxiv:2605.09782 v2 · 2026-05-10 · cs.DS · stat.ME

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\usepackage{pith}
\pithnumber{Y42FOHJD636FNGP27W3L6ZPQI6}

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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

GenusSink provides near-linear time (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory for approximate generalized Sinkhorn algorithms with shortest-path-distance costs on bounded genus graphs, and is numerically equivalent to the brute-force geodesic Sinkhorn algorithm on n-vertex graphs with treewidth O(log log n).

C2weakest assumption

Bounded-genus graphs admit separator decompositions that allow approximation of their metrics by small-treewidth metrics while preserving the structure needed for fast generalized distance matrix multiplications without accumulating unacceptable error in the Sinkhorn iterations.

C3one line summary

GenusSink achieves near-linear time approximate generalized Sinkhorn for geodesic optimal transport on bounded-genus graphs by combining separator-based decompositions with Fourier and low-displacement-rank matrix-vector multiplications.

Receipt and verification

First computed	2026-05-20T00:05:46.803628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c734571d23f6fc5699fafdb6bf65f047ae5f325c3d5b1efcd4e29aa9ed6a9b7b

Aliases

arxiv: 2605.09782 · arxiv_version: 2605.09782v2 · doi: 10.48550/arxiv.2605.09782 · pith_short_12: Y42FOHJD636F · pith_short_16: Y42FOHJD636FNGP2 · pith_short_8: Y42FOHJD

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/Y42FOHJD636FNGP27W3L6ZPQI6 \
  | 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: c734571d23f6fc5699fafdb6bf65f047ae5f325c3d5b1efcd4e29aa9ed6a9b7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b9b47fc4942d71929d7fd8f56aa9d70d8409c2e0ccf478d35560f28e09fb5a5",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-10T22:00:42Z",
    "title_canon_sha256": "966a4fbefcc228d5e38205447f001f520a1b9299bfc4b8153abd97c054e0190f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09782",
    "kind": "arxiv",
    "version": 2
  }
}