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Incremental Submodular Maximization: Better Than Greedy

Authors Marcin Bienkowski , Joakim Blikstad , Jarosław Byrka , Martín Costa , Yann Disser , Annette Lutz

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Subject Classification

ACM Subject Classification
  • Theory of computation → Submodular optimization and polymatroids
  • Theory of computation → Online algorithms
Keywords
  • Submodular maximization
  • incremental optimization
  • competitive analysis

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Abstract

We consider submodular maximization under increasing cardinality constraint and ask for a good incremental solution, i.e., an ordering of the ground set such that each prefix of the ordering yields a good solution for its respective cardinality. A classical result in this setting is that the greedy algorithm achieves a competitive ratio, i.e., an approximation guarantee across all cardinalities, of e/(e-1) ≈ 1.582. No better general guarantee was previously known. We present an adaptive scaling algorithm achieving a competitive ratio of 1.373. We complement our result by a lower bound of 1.25 on the best possible deterministic competitive ratio for incremental submodular maximization.

Cite As Get BibTex

Marcin Bienkowski, Joakim Blikstad, Jarosław Byrka, Martín Costa, Yann Disser, and Annette Lutz. Incremental Submodular Maximization: Better Than Greedy. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 134:1-134:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.134

Author Details

Marcin Bienkowski
  • University of Wrocław, Poland
Joakim Blikstad
  • CWI, Amsterdam, The Netherlands
Jarosław Byrka
  • University of Wrocław, Poland
Martín Costa
  • University of Warwick, UK
Yann Disser
  • TU Darmstadt, Germany
Annette Lutz
  • TU Darmstadt, Germany

Funding

This research has been initiated at the AlgUW Workshop (Bedlewo 09.2025), supported by the Excellence Initiative - Research University (IDUB) funds of the University of Warsaw.
  • Bienkowski, Marcin: Supported by Polish National Science Centre grant 2022/45/B/ST6/00559.
  • Byrka, Jarosław: Supported by Polish National Science Centre grant 2020/39/B/ST6/01641.
  • Disser, Yann: Supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through subproject A09 of CRC/TRR154.
  • Lutz, Annette: Supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through subproject A09 of CRC/TRR154.

References

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