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On Maximizing a Weakly Submodular Function over a Matroid Constraint via the Greedy Algorithm — arXiv:2609.05008

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05008
License (as archived): CC0-1.0
Archived: 2026-10-16T23:52:49.330Z
SHA-256 of the archived text: 033078ab21f1bf22af29d21a880c5d15609133e9545e4d5bc247a34f81f30fc5
Stable URL of this page: https://metraipolis.com/documento/dc_f8f6996478ef

How to cite

On Maximizing a Weakly Submodular Function over a Matroid Constraint via the Greedy Algorithm — arXiv:2609.05008 — arXiv (en), https://arxiv.org/abs/2609.05008 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f8f6996478ef (Metraipolis archive dc_f8f6996478ef, sha256 033078ab21f1bf22af29d21a880c5d15609133e9545e4d5bc247a34f81f30fc5)

BibTeX

@misc{dcf8f6996478ef,
  title = {On Maximizing a Weakly Submodular Function over a Matroid Constraint via the Greedy Algorithm — arXiv:2609.05008},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05008},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f8f6996478ef; sha256 033078ab21f1bf22af29d21a880c5d15609133e9545e4d5bc247a34f81f30fc5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05008. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider the problem of approximately maximizing a weakly submodular function using the standard greedy algorithm, which is known to give tight approximation results for such functions under a cardinality constraint. We show that this is not the case for general matroid constraints. For any $\gamma < 1$, we give a family of $\gamma$-weakly submodular functions and a simple partition matroid constraint and show that the standard greedy algorithm provides no constant approximation for the resulting constrained maximization problem.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-07 in cs.DS).
Categorie arXiv: Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.05008 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T23:22:37.569Z dalla pagina https://arxiv.org/catchup/cs.DS/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).