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- W4383472968 abstract "We study the uniform $2$-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated with a $2$-dimensional weight vector and a positive profit, along with $m$ $2$-dimensional bins of uniform (unit) capacity in each dimension. The goal is to find an assignment of a subset of the items to the bins, such that the total weight of items assigned to a single bin is at most one in each dimension, and the total profit is maximized. Our main result is a $(1- frac{ln 2}{2} - varepsilon)$-approximation algorithm for 2VMK, for every fixed $varepsilon > 0$, thus improving the best known ratio of $(1 - frac{1}{e}-varepsilon)$ which follows as a special case from a result of [Fleischer at al., MOR 2011]. Our algorithm relies on an adaptation of the Round$&$Approx framework of [Bansal et al., SICOMP 2010], originally designed for set covering problems, to maximization problems. The algorithm uses randomized rounding of a configuration-LP solution to assign items to $approx mcdot ln 2 approx 0.693cdot m$ of the bins, followed by a reduction to the ($1$-dimensional) Multiple Knapsack problem for assigning items to the remaining bins." @default.
- W4383472968 created "2023-07-07" @default.
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- W4383472968 date "2023-07-05" @default.
- W4383472968 modified "2023-10-14" @default.
- W4383472968 title "Improved Approximation for Two-dimensional Vector Multiple Knapsack" @default.
- W4383472968 doi "https://doi.org/10.48550/arxiv.2307.02137" @default.
- W4383472968 hasPublicationYear "2023" @default.
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