Pith Number

pith:TKHVJR2L

pith:2026:TKHVJR2LGOKQXX3LFHGKAAVKJK

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The Impossibility of Simultaneous Time and I/O Optimality for The Planar Maxima and Convex Hull Problems

Gerth St{\o}lting Brodal, Nodari Sitchinava, Peyman Afshani

No deterministic output-sensitive algorithm achieves both optimal time and optimal I/O for planar convex hull and maxima.

arxiv:2605.09464 v2 · 2026-05-10 · cs.DS · cs.CG

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\pithnumber{TKHVJR2LGOKQXX3LFHGKAAVKJK}

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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 prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes.

C2weakest assumption

The lower bound holds in the standard external-memory model where time and I/O complexities are measured separately and optimality is defined with respect to input size n and output size h.

C3one line summary

No deterministic output-sensitive algorithm for planar maxima or convex hull can simultaneously achieve optimal time and I/O complexity.

Receipt and verification

First computed	2026-05-21T01:05:20.806715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a8f54c74b33950bdf6b29cca002aa4a8f8bb81211f03ff2e289e0bfd45befd1

Aliases

arxiv: 2605.09464 · arxiv_version: 2605.09464v2 · doi: 10.48550/arxiv.2605.09464 · pith_short_12: TKHVJR2LGOKQ · pith_short_16: TKHVJR2LGOKQXX3L · pith_short_8: TKHVJR2L

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TKHVJR2LGOKQXX3LFHGKAAVKJK \
  | 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: 9a8f54c74b33950bdf6b29cca002aa4a8f8bb81211f03ff2e289e0bfd45befd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eae949c7d2787399405ad916240383868c1125de3f56e04f2caeecb76cc9174",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-10T10:31:45Z",
    "title_canon_sha256": "ebb284da50cfa1175724401da82000f917e313d04b62d3cb5fb11e8a148bb036"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09464",
    "kind": "arxiv",
    "version": 2
  }
}