Team formation problem is a very important problem in the labor market, and it is proved to be NP-hard. In this paper, we design an efficient bicriteria streaming algorithms to construct a balance between gain and cost in a team formation problem with cardinality constraint on the integer lattice. To solve this problem, we establish a model for maximizing the difference between a nonnegative normalized monotone submodule function and a nonnegative linear function. Further, we discuss the case where the first function of the object function is $\alpha$--weakly submodular. Combining the lattice binary search with the threshold method, we present an online algorithm called bicriteria streaming algorithms. Meanwhile, we give detailed analysis for both of these models.

翻译：团队形成问题是劳动力市场中一个非常重要的问题，已被证明是NP难的。本文设计了一种高效的双目标流式算法，用于在整数格上具有基数约束的团队形成问题中平衡增益与成本。为解决该问题，我们建立了一个模型，旨在最大化非负归一化单调子模函数与非负线性函数之间的差值。此外，我们还讨论了目标函数中第一个函数为$\alpha$-弱子模的情形。通过将格点二分搜索与阈值方法相结合，我们提出了一种称为双目标流式算法的在线算法。同时，我们对这两种模型均给出了详细的分析。