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Incremental Maximization for a Broad Class of Objectives

Authors Yann Disser , David Weckbecker

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LIPIcs.ESA.2025.92.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Combinatorial optimization
Keywords
  • incremental maximization
  • competitive analysis
  • subadditive functions

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Abstract

We consider incremental maximization problems, where the solution has to be built up gradually by adding elements one after the other. In every step, the incremental solution must be competitive, compared against the optimum solution of the current cardinality. We prove that a competitive solution always exists when the objective function is monotone and β-accountable, by providing a scaling algorithm that guarantees a constant competitive ratio. This generalizes known results and, importantly, yields the first competitive algorithm for the natural class of monotone and subadditive objective functions.

Cite As Get BibTex

Yann Disser and David Weckbecker. Incremental Maximization for a Broad Class of Objectives. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 92:1-92:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.92

Author Details

Yann Disser
  • TU Darmstadt, Germany
David Weckbecker
  • TU Darmstadt, Germany

Funding

Supported by DFG grant DI 2041/2.

References

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