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Fixed-Parameter Tractable Submodular Maximization over a Matroid

Authors Shamisa Nematollahi , Adrian Vladu , Junyao Zhao

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LIPIcs.ITCS.2026.105.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Submodular maximization
  • matroids
  • parameterized complexity
  • streaming algorithms

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Abstract

In this paper, we design fixed-parameter tractable (FPT) algorithms for (non-monotone) submodular maximization subject to a matroid constraint, where the matroid rank r is treated as a fixed parameter that is independent of the total number of elements n. We provide two FPT algorithms: one for the offline setting and another for the random-order streaming setting. Our streaming algorithm achieves a 1/2-ε approximation using Õ(r/poly(ε)) memory, while our offline algorithm obtains a 1-(1)/(e)-ε approximation with n⋅ 2^{Õ(r/poly(ε))} runtime and Õ(r/poly(ε)) memory. Both approximation factors are near-optimal in their respective settings, given existing hardness results. In particular, our offline algorithm demonstrates that - unlike in the polynomial-time regime - there is essentially no separation between monotone and non-monotone submodular maximization under a matroid constraint in the FPT framework.

Cite As Get BibTex

Shamisa Nematollahi, Adrian Vladu, and Junyao Zhao. Fixed-Parameter Tractable Submodular Maximization over a Matroid. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 105:1-105:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.105

Author Details

Shamisa Nematollahi
  • CNRS, IRIF, Université Paris Cité, Paris, France
Adrian Vladu
  • CNRS, IRIF, Université Paris Cité, Paris, France
Junyao Zhao
  • CNRS, IRIF, Université Paris Cité, Paris, France

Funding

  • Nematollahi, Shamisa: Partially supported by the French Agence Nationale de la Recherche (ANR) under grant ANR-21-CE48-0016 (project COMCOPT).
  • Vladu, Adrian: Partially supported by the French Agence Nationale de la Recherche (ANR) under grant ANR-21-CE48-0016 (project COMCOPT).
  • Zhao, Junyao: Supported by a postdoctoral fellowship from the Fondation Sciences Mathématiques de Paris (FSMP).

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