本文研究在基数约束下具有单调性的次模+超模函数最大化问题的流模型。该问题在数据处理、机器学习和人工智能等方面都有广泛应用。借助于目标函数的收益递减率（$\gamma$），我们设计了单轮读取数据的过滤-流算法，并结合次模、超模函数的全局曲率（$\kappa^{g}$）得到算法的近似比为$\min\left\{\frac{（1-\varepsilon）\gamma}{2^{\gamma}}，1-\frac{\gamma}{2^{\gamma}（1-\kappa^{g}）^{2}}\right\}$。数值实验验证了过滤-流算法对BP最大化问题的有效性并且得出：次模函数和超模函数在同量级条件下，能保证在较少的时间内得到与贪婪算法相同的最优值。

In this paper, wepropose streaming algorithms for the maximization ofsubmodular+supermodular functions with cardinality constraint, whichhas wide applications in data processing, machine learning andartificial intelligence. By means of the diminishing return ratioof the objective function, we design a one-pass sieve-streamingalgorithm and get the approximate ratio $\min\left\{\frac{(1-\varepsilon)\gamma}{2^{\gamma}}, 1-\frac{\gamma}{2^{\gamma}(1-\kappa^{g})^{2}}\right\}$. Numerical experiments show that the sieve-streaming algorithm is effective forthe BP-maximization problem and can guarantee the same result asthe greedy algorithm with less time if submodular function andsupermodular are in the same order of magnitude.