Author

Shengminjie Chen

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Preprint Sep 2026

Breaking the 1/3 Barrier for constrained $\boldsymbol{k}$-Submodular Maximization: A Proportional Top-2 Randomized Framework

$k$-submodularity generalizes submodularity by allowing each selected element to be assigned one of $k$ labels. We study the maximization of a non-monotone $k$-submodular function, where $k\ge2$, under matroid and knapsack constraints. We develop a proportional top-2 randomized framework that achieves an approximation...

Si-Yuan Chen, Shengminjie Chen, Sui-Xiang Gao et al. · 0 citations

Preprint Sep 2026

Breaking the 1/3 Barrier for $\boldsymbol{k}$-Submodular Maximization under Matroid and Knapsack Constraints: A Proportional Top-2 Randomized Framework

These results give the first approximation guarantees exceeding $1/3$ for non-monotone $k$-submodular maximization under matroid and knapsack constraints under classical support constraints.

Si-Yuan Chen, Shengminjie Chen, Sui-Xiang Gao et al. · 0 citations