Pith Number

pith:GOJUNSBC

pith:2026:GOJUNSBCBRB3GMH3FTTZIYIGRQ

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Optimizing Line Segment Inspection with Limited-Range Drones

Alina Kasiuk, Inmaculada Ventura, Jos\'e-Manuel Higes, Jos\'e-Miguel D\'iaz-B\'a\~nez

The drone inspection problem for line segments is strongly NP-hard even with two drones on a straight line.

arxiv:2605.15765 v1 · 2026-05-15 · cs.CG · cs.DS · cs.RO · math.OC

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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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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 are able to prove that this optimization problem is strongly NP-hard even when the segments are positioned on a line and the scenario involves only two drones.

C2weakest assumption

The model assumes that battery limits force periodic returns to a single fixed base station and that the objective of minimizing makespan accurately reflects operational priorities without additional constraints such as wind, obstacles, or variable inspection times.

C3one line summary

The authors prove strong NP-hardness for inspecting line segments on a line with two limited-range drones and propose approximation algorithms that achieve near-optimal makespan in experiments.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] Annals of Operations Research , pages= 2023

[2] Operational Research , volume= 2022

[3] European Journal of Operational Research , volume= 2024

[4] Information Processing Letters , pages= 2024

[5] Theoretical Computer Science , volume= 2022

Receipt and verification

First computed	2026-05-20T00:01:17.072427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

339346c8220c43b330fb2ce79461068c2816c6c1b6d02a127f842da41d9bfd25

Aliases

arxiv: 2605.15765 · arxiv_version: 2605.15765v1 · doi: 10.48550/arxiv.2605.15765 · pith_short_12: GOJUNSBCBRB3 · pith_short_16: GOJUNSBCBRB3GMH3 · pith_short_8: GOJUNSBC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GOJUNSBCBRB3GMH3FTTZIYIGRQ \
  | 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: 339346c8220c43b330fb2ce79461068c2816c6c1b6d02a127f842da41d9bfd25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e31b62dac648fd944d8d406310c73524a259018906062fe0dfd2aa0e191d6d26",
    "cross_cats_sorted": [
      "cs.DS",
      "cs.RO",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-05-15T09:24:50Z",
    "title_canon_sha256": "22e65947f9119ede3f2271b038b34414274ec97ca2f34edc04f9eecdd44b2d6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15765",
    "kind": "arxiv",
    "version": 1
  }
}