Pith Number

pith:ZRLTCAO7

pith:2026:ZRLTCAO7TUIEWYCPYB43YRQ2PY

not attested not anchored not stored refs resolved

Hitting Axis-Parallel Segments with Weighted Points

Jatin Yadav, Rajiv Raman, Siddhartha Sarkar

An LP-rounding algorithm achieves a randomized (1 + 2/e)-approximation for hitting weighted axis-parallel segments, breaking the factor-2 barrier.

arxiv:2605.14499 v1 · 2026-05-14 · cs.CG · cs.DS

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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 present an LP-rounding algorithm that breaks the factor-2 barrier. For the weighted problem, we obtain a randomized (1+2/e)-approximation by combining systematic rounding on horizontal lines with an exact repair step on residual vertical sub-instances.

C2weakest assumption

The LP relaxation admits an efficient solution whose fractional optimum is within a constant factor of the integral optimum, and that the rounding analysis holds without additional assumptions on point or segment positions beyond axis-parallelism.

C3one line summary

An LP-rounding algorithm yields a randomized (1 + 2/e)-approximation for weighted hitting set of axis-parallel segments, with a (1 + 1/(e-1)) bound in the unweighted case and 1 + 1/e when one orientation consists of lines.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] Approximationschemesforindependent set and sparse subsets of polygons.Journal of the ACM, 66(4):29:1–29:40, 2019 2019

[2] A non-linear lower bound for planar epsilon-nets.Discret 2012

[3] Small-sizeϵ-nets for axis-parallel rectangles and boxes.SIAM J 2010

[4] Katz, Gila Morgenstern, and Yelena Yuditsky 2013

[5] On the number of points in general position in the plane 2018

Receipt and verification

First computed	2026-05-17T23:39:06.337154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc573101df9d104b604fc079bc461a7e0d79edf1573de58378c17b95ae5028df

Aliases

arxiv: 2605.14499 · arxiv_version: 2605.14499v1 · doi: 10.48550/arxiv.2605.14499 · pith_short_12: ZRLTCAO7TUIE · pith_short_16: ZRLTCAO7TUIEWYCP · pith_short_8: ZRLTCAO7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZRLTCAO7TUIEWYCPYB43YRQ2PY \
  | 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: cc573101df9d104b604fc079bc461a7e0d79edf1573de58378c17b95ae5028df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f434d680cb49f07d37717a213b94d62451753a0be2a6cd9111786a092966c33b",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-05-14T07:38:53Z",
    "title_canon_sha256": "892c44f7c22756dd1daf270084526279826f90703fbf6a1bca9cab893fd5ad3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14499",
    "kind": "arxiv",
    "version": 1
  }
}