Maximizing non-monotone submodular set functions subject to different constraints: Combined algorithms

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Different constraints that we study are exact cardinality and multiple knapsack constraints for which we achieve (0.25−ϵ)(0.25−ϵ)-factor algorithms.We also show, as our main contribution, how to use the continuous greedy process for non-monotone functions and, as a result, obtain a 0.13-factor approximation algorithm for maximization over any solvable down-monotone polytope.