Using maximum coverage to optimize recommendation systems in e-commerce

We study the problem of optimizing recommendation systems for e-commerce sites. We consider in particular a combinatorial solution to this optimization based on the well known Maximum Coverage problem that asks for the k sets (products) that cover the most elements from a ground set (consumers). This formulation provides an abstract model for what k products should be recommended to maximize the probability of consumer purchase. Unfortunately, Maximum Coverage is NP-complete but an efficient approximation algorithm exists based on the Greedy methodology.