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arXiv · 2207.01551

Correlated Stochastic Knapsack with a Submodular Objective

Sheng Yang·Samir Khuller·Sunav Choudhary·Subrata Mitra·Kanak Mahadik
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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 $(1 - 1/\sqrt{e})/2 \simeq 0.1967$ approximation algorithm with or without those additional constraints, eliminating the need of a key assumption and improving on the $(1 - 1/\sqrt[4]{e})/2 \simeq 0.1106$ approximation by Fukunaga et al. [AAAI 2019].

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Sheng Yang, Samir Khuller, Sunav Choudhary, Subrata Mitra, Kanak Mahadik. 2022-07-04. Correlated Stochastic Knapsack with a Submodular Objective. https://arxiv.org/abs/2207.01551

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