Coupled and k-Sided Placements: Generalizing Generalized Assignment

In modern data centers and cloud computing systems, jobs often require resources distributed across nodes providing a wide variety of services. Motivated by this, we study the Coupled Placement problem, in which we place jobs into computation and storage nodes with capacity constraints, so as to optimize some costs or profits associated with the placement. The coupled placement problem is a natural generalization of the widely-studied generalized assignment problem (GAP), which concerns the placement of jobs into single nodes providing one kind of service. We also study a further generalization, the k-Sided Placement problem, in which we place jobs into k-tuples of nodes, each node in a tuple offering one of k services.