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Motivated by current trends in cloud computing, we study a version of thegeneralized assignment problem where a set of virtual processors has to beimplemented by a set of identical processors. For literature consistency, wesay that a set of virtual machines (VMs) is assigned to a set of physicalmachines (PMs). The optimization criteria is to minimize the power consumed byall the PMs. We term the problem Virtual Machine Assignment (VMA). Crucialdifferences with previous work include a variable number of PMs, that each VMmust be assigned to exactly one PM (i.e., VMs cannot be implementedfractionally), and a minimum power consumption for each active PM. Suchinfrastructure may be strictly constrained in the number of PMs or in the PMs'capacity, depending on how costly (in terms of power consumption) is to add anew PM to the system or to heavily load some of the existing PMs. Low usage orample budget yields models where PM capacity and/or the number of PMs may beassumed unbounded for all practical purposes. We study 4 VMA problems dependingon whether the capacity or the number of PMs is bounded or not. Specifically,we study hardness and online competitiveness for a variety of cases. To thebest of our knowledge, this is the first comprehensive study of the VMA problemfor this cost function.

Power-efficient Assignment of Virtual Machines to Physical Machines