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arXiv · 2105.15159

On maximizing a monotone $k$-submodular function under a knapsack constraint

Zhongzheng Tang·Chenhao Wang·Hau Chan
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Abstract

We study the problem of maximizing a non-negative monotone $k$-submodular function $f$ under a knapsack constraint, where a $k$-submodular function is a natural generalization of a submodular function to $k$ dimensions. We present a deterministic $(\frac12-\frac{1}{2e})\approx 0.316$-approximation algorithm that evaluates $f$ $O(n^4k^3)$ times, based on the result of Sviridenko (2004) on submodular knapsack maximization.

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Zhongzheng Tang, Chenhao Wang, Hau Chan. 2021-05-31. On maximizing a monotone $k$-submodular function under a knapsack constraint. https://arxiv.org/abs/2105.15159

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