Pith Number

pith:4KMVE3OY

pith:2026:4KMVE3OYCFNKYWTKSP3ZQTBAVL

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On the parameterized complexity of Broadcast Independence and Broadcast Packing

Anthony Perez, Edouard Nemery, Florian Sikora, Joanne Dumont

Broadcast Independence and Broadcast Packing are FPT when parameterized by treewidth plus diameter.

arxiv:2605.16001 v1 · 2026-05-15 · cs.DS · cs.CC · cs.DM

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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 Broadcast Independence and Broadcast Packing are FPT parameterized by the treewidth plus the diameter of G, with a family of dynamic-programming algorithms over nice tree decompositions.

C2weakest assumption

The input graph admits a nice tree decomposition of width equal to the treewidth parameter and the eccentricity function can be precomputed in polynomial time for the DP states; this is invoked when the authors state the DP runs over nice tree decompositions in the FPT algorithm section.

C3one line summary

Broadcast Independence and Broadcast Packing are FPT parameterized by treewidth plus diameter via DP on nice tree decompositions, W[1]-hard for pathwidth, and admit a constant-factor approximation parameterized by treewidth.

References

24 extracted · 24 resolved · 1 Pith anchors

[1] Broadcasts on paths and cycles , journal = 2020 · doi:10.1016/j.dam.2020.01.030

[2] Hiroshi Eto and Fengrui Guo and Eiji Miyano , title =. J. Comb. Optim. , volume =. 2014 , url =. doi:10.1007/S10878-012-9594-4 , timestamp = 2014 · doi:10.1007/s10878-012-9594-4

[3] arXiv preprint arXiv:2305.03516 , year=

[4] Journal of Combinatorial Optimization , volume= 2014

[5] International Workshop on Graph-Theoretic Concepts in Computer Science , pages= 2016

Receipt and verification

First computed	2026-05-20T00:01:48.436920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e299526dd8115aac5a6a93f7984c20aaca8e723d1af4f855401c94f65d7db55a

Aliases

arxiv: 2605.16001 · arxiv_version: 2605.16001v1 · doi: 10.48550/arxiv.2605.16001 · pith_short_12: 4KMVE3OYCFNK · pith_short_16: 4KMVE3OYCFNKYWTK · pith_short_8: 4KMVE3OY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4KMVE3OYCFNKYWTKSP3ZQTBAVL \
  | 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: e299526dd8115aac5a6a93f7984c20aaca8e723d1af4f855401c94f65d7db55a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29cd7e1dcc29fc25fa94862953410593158b62d66f7ae054b81991c46317935f",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-15T14:31:51Z",
    "title_canon_sha256": "55ae2be069046db68c3acdbafe8616cbf610035c0bdad7bddd18279522c577a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16001",
    "kind": "arxiv",
    "version": 1
  }
}