In this paper, we study the problem of maximizing k-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a 21(1−e−2)≈0.432 greedy approximation algorithm. For the non-monotone case, we are the first to consider the knapsack problem and provide a greedy-type combinatorial algorithm with approximation ratio 31(1−e−3)≈0.317.
@article{arxiv.2306.14520,
title = {Approximation algorithms for $k$-submodular maximization subject to a knapsack constraint},
author = {Hao Xiao and Qian Liu and Yang Zhou and Min Li},
journal= {arXiv preprint arXiv:2306.14520},
year = {2023}
}