License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.49
URN: urn:nbn:de:0030-drops-171711
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17171/
Go to the corresponding LIPIcs Volume Portal

Klimm, Max ; Knaack, Martin

Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint

pdf-format:
LIPIcs-APPROX49.pdf (0.7 MB)

Abstract

This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness factor of a policy is the worst case ratio of the solution obtained by following the policy and an optimal solution that knows the knapsack capacity. We develop an algorithm with a robustness factor that is decreasing in the curvature c of the submodular function. For the extreme cases c = 0 corresponding to a modular objective, it matches a previously known and best possible robustness factor of 1/2. For the other extreme case of c = 1 it yields a robustness factor of ≈ 0.35 improving over the best previously known robustness factor of ≈ 0.06.

BibTeX - Entry

@InProceedings{klimm_et_al:LIPIcs.APPROX/RANDOM.2022.49,
  author =	{Klimm, Max and Knaack, Martin},
  title =	{{Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{49:1--49:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17171},
  URN =		{urn:nbn:de:0030-drops-171711},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.49},
  annote =	{Keywords: submodular function, knapsack, approximation algorithm, robust optimization}
}

Keywords: submodular function, knapsack, approximation algorithm, robust optimization
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)
Issue Date: 2022
Date of publication: 15.09.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI