Streaming algorithm for balance gain and cost with cardinality constraint on the integer lattice

The team formation problem is a very important problem in the labor market that has been proved to be NP-hard. This paper proposes an efficient bicriteria streaming algorithm aimed at striking a balance between gain and cost in team formation problems with cardinality constraints on the integer lattice. To address this, we utilized a model optimized for maximizing the difference between a nonnegative normalized monotone submodular function and a nonnegative linear function. We further consider the case where the first function of the object function is weakly submodular. Combining the lattice binary search with the threshold method, we present an online algorithm called bicriteria streaming algorithmsalgorithm. Concomitantly, we comprehensively analyze both models.