We consider the problem of maximizing a non-negative submodular function under the b-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of \(2+\varepsilon \) , \(3 + 2 \sqrt{2} \approx 5.828\) , and \(4 + 2 \sqrt{3} \approx 7.464\) , respectively. We also consider a generalized problem, where a k-uniform hypergraph is given, along with an extra matroid or a \(k'\) -matchoid constraint imposed on the edges, with the same goal of finding a b-matching that maximizes a submodular function. When the extra constraint is a matroid, we obtain the approximation ratios of \(k + 1 + \varepsilon \) , \(k + 2\sqrt{k+1} + 2\) , and \(k + 2\sqrt{k + 2} + 3\) for linear, monotone and non-monotone submodular functions, respectively. When the extra constraint is a \(k'\) -matchoid, we attain the approximation ratio \(\frac{8}{3}k+ \frac{64}{9}k' + O(1)\) for general submodular functions.
