Streaming Based Bicriteria Approximation Algorithms for Submodular Optimization

This paper proposes the optimization problem Non-Monotone Submodular Cover (SCP), which is to minimize the cost required to ensure that a non-monotone submodular benefit function exceeds a given threshold. Two algorithms are presented for SCP that both give a bicriteria approximation guarantee to the problem. Both algorithms process the ground set in a stream, one in multiple passes. Further, a bicriteria approximation algorithm is given for the related Non-Monotone Submodular Maximization subject to a knapsack constraint optimization problem.