The authors introduce two new submodular optimization problems and 
investigate approximation algorithms for them. The problems are 
natural generalizations of many previous problems: there is a covering 
problem ($min\\{ f(X) : g(X) \ge c\\}$) and a packing or knapsack problem 
($max\\{ g(X) : f(X) \le b\\}$), where both f and g are submodular. These 
generalize well-known previously studied versions of the problems 
usually assume that f is modular. They show that there is an intimate 
relationship between the two problems: any polynomial-time 
bi-criterion algorithm for one problem implies one for the other 
problem (with similar approximation factors) using a simple reduction. 
They then present a general iterative framework for solving the two 
problems by replacing either f or g by tight upper or lower bounds 
(often modular) at each iteration. These tend to reduce the problem 
at each iteration to a simpler subproblem for which there are existing 
algorithms with approximation guarantees. In many cases, they are able 
to translate these into approximation guarantees for the more general 
problem. Their approximation bounds are curvature-dependent and 
highlight the importance of this quantity on the difficulty of the 
problem. The authors also present a hardness result that matches their 
best approximation guarantees up to log factors, show that a number of 
existing approximation algorithms (e.g. greedy ones) for the simpler 
problem variants can be recovered from their framework by using 
specific modular bounds, and show experimentally that the simpler 
algorithm variants may perform as well as the ones with better 
approximation guarantees in practice.