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.
Submodular maximization meets streaming: matchings, matroids, and more.Mathematical Programming, 154(1-2):225–247, 2015
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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.