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arXiv · 2102.05854

Approximation Algorithms for Generalized Multidimensional Knapsack

Arindam Khan·Eklavya Sharma·K. V. N. Sreenivas
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Abstract

We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack. The goal is to find a non-overlapping axis-parallel packing of a subset of items into the given knapsack such that the vector constraints are not violated, i.e., the sum of weights of all the packed items in any of the $d$ dimensions does not exceed one. We consider two variants of the problem: $(i)$ the items are not allowed to be rotated, $(ii)$ items can be rotated by 90 degrees. We give a $(2+\epsilon)$-approximation algorithm for this problem (both versions). In the process, we also study a variant of the maximum generalized assignment problem (Max-GAP), called Vector-Max-GAP, and design a PTAS for it.

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Arindam Khan, Eklavya Sharma, K. V. N. Sreenivas. 2021-02-11. Approximation Algorithms for Generalized Multidimensional Knapsack. https://arxiv.org/abs/2102.05854

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