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DOI: 10.4230/LIPIcs.ESA.2022.91
Correlated Stochastic Knapsack with a Submodular Objective

Authors: Sheng Yang, Samir Khuller, Sunav Choudhary, Subrata Mitra, and Kanak Mahadik

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear constraints from Ma [Mathematics of Operations Research, Volume 43(3), 2018] on correlated stochastic knapsack problem. The relaxation is then solved by the stochastic continuous greedy algorithm, and rounded by a novel method to fit the contention resolution scheme (Feldman et al. [FOCS 2011]). We obtain a pseudo-polynomial time (1 - 1/√e)/2 ≃ 0.1967 approximation algorithm with or without those additional constraints, eliminating the need of a key assumption and improving on the (1 - 1/∜e)/2 ≃ 0.1106 approximation by Fukunaga et al. [AAAI 2019].
Cite as

Sheng Yang, Samir Khuller, Sunav Choudhary, Subrata Mitra, and Kanak Mahadik. Correlated Stochastic Knapsack with a Submodular Objective. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 91:1-91:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{yang_et_al:LIPIcs.ESA.2022.91,
  author =	{Yang, Sheng and Khuller, Samir and Choudhary, Sunav and Mitra, Subrata and Mahadik, Kanak},
  title =	{{Correlated Stochastic Knapsack with a Submodular Objective}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{91:1--91:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.91},
  URN =		{urn:nbn:de:0030-drops-170296},
  doi =		{10.4230/LIPIcs.ESA.2022.91},
  annote =	{Keywords: Stochastic Knapsack, Submodular Optimization, Stochastic Optimization}
}
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