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DOI: 10.4230/LIPIcs.ESA.2026.4

Data-Dependent Evaluations for Budgeted Submodular Maximization

Authors: Lejian Zhang, Xueyan Tang, and Jing Tang

Published in: LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026)

Abstract

Submodular maximization is an important building block for developing algorithms in many areas such as machine learning and data mining. Due to the NP-hardness of the problem, analysis of submodular maximization algorithms typically provides pessimistic worst-case approximation factors only. It is not easy to evaluate how close a produced solution is to an optimal one for a given problem instance. In this paper, we develop new data-dependent upper bounds for submodular maximization with a knapsack constraint. We theoretically prove that they dominate the optimal solution and empirically demonstrate their advantages in certifying how close to optimal a solution is through experiments with real-world datasets.

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Lejian Zhang, Xueyan Tang, and Jing Tang. Data-Dependent Evaluations for Budgeted Submodular Maximization. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{zhang_et_al:LIPIcs.ESA.2026.4,
  author =	{Zhang, Lejian and Tang, Xueyan and Tang, Jing},
  title =	{{Data-Dependent Evaluations for Budgeted Submodular Maximization}},
  booktitle =	{34th Annual European Symposium on Algorithms (ESA 2026)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-445-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{388},
  editor =	{Bille, Philip and Pettie, Seth and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.4},
  URN =		{urn:nbn:de:0030-drops-271407},
  doi =		{10.4230/LIPIcs.ESA.2026.4},
  annote =	{Keywords: submodular maximization, knapsack constraint, approximation guarantee}
}

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Data-Dependent Evaluations for Budgeted Submodular Maximization

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