A hybrid algorithm achieves <0.819k + O(sqrt(k)) approximation for submodular maximization over k-matroid intersection, the first multiplicative improvement over the greedy (k+1) ratio for general k.
Asymptotically optimal hardness fork-set packing and k-matroid intersection
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Submodular Maximization over a Matroid $k$-Intersection: Multiplicative Improvement over Greedy
A hybrid algorithm achieves <0.819k + O(sqrt(k)) approximation for submodular maximization over k-matroid intersection, the first multiplicative improvement over the greedy (k+1) ratio for general k.