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.
A parameterized view on matroid optimization problems.Theoretical Computer Science, 410(44):4471–4479
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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.