Online Bicriteria Algorithms to Balance Coverage and Cost in Team Formation

In this paper, we investigate the team formation problem to balance the coverage gained and the cost incurred. This problem can be formulated as maximizing the difference of two set functions \(f-l\), where f is non-negative monotone approximately submodular function, and l is non-negative linear function. We propose three online bicriteria algorithms. The first two handle the cases where the function f is \(\gamma \)-weakly submodular, and strictly \(\gamma \)-weakly submodular, respectively. The last algorithm integrates the first two with more parameters introduced.