Data Center Scheduling, Generalized Flows, and Submodularity

Inspired by problems in data center scheduling, we study the submodularity of certain scheduling problems as a function of the set of machine capacities and the corresponding implications. In particular, we • give a short proof that, as a function of the excess vector, maximum generalized flow is submodular and minimum cost generalized flow is supermodular; • extend Wolsey's approximation guarantees for submodular covering problems to a new class of problems we call supermodular packing problems; • use these results to get tighter approximation guarantees for several data center scheduling problems.