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

Zhongzheng Tang; Chenhao Wang; Hau Chan

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

Data Structures and Algorithms 2023-08-04 v2 Discrete Mathematics Optimization and Control

Authors: Zhongzheng Tang , Chenhao Wang , Hau Chan

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.

Keywords

submodular maximization approximation algorithm

Cite

@article{arxiv.2105.15159,
  title  = {On maximizing a monotone $k$-submodular function under a knapsack constraint},
  author = {Zhongzheng Tang and Chenhao Wang and Hau Chan},
  journal= {arXiv preprint arXiv:2105.15159},
  year   = {2023}
}

Comments

This manuscript is published in Operations Research Letters, but there is an error in the proof of Theorem 1. We provide a corrigendum in the end of this manuscript

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

Abstract

Keywords

Cite

Comments

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