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 α--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.
@article{arxiv.2402.10298,
title = {Streaming algorithm for balance gain and cost with cardinality constraint on the integer lattice},
author = {Jingjing Tan},
journal= {arXiv preprint arXiv:2402.10298},
year = {2024}
}