1. A system, comprising: at least one computing device that implements one or more services, wherein the one or more services: obtain a first representation of a network, the network comprising a plurality of computing devices and the first representation of the network indicating network connections between devices in the network; obtain a second representation of a set of one or more component placement requests, the set of one or more component placement requests comprising requests to instantiate a plurality of components, the second representation indicating constraints on connectivity between components of the plurality of components; process the first representation and one or more connection metrics to generate a third representation of the network that indicates fewer network connections than the first representation; allocate a component associated with the second representation to a location associated with the third representation; process the third representation, the constraints, and the allocated component to generate a placement solution that includes a different location, in the third representation, of at least one other component based at least in part on the component, the location allocated to the component, and the constraints; and implement the placement solution by at least using a set of the plurality of computing devices to instantiate the plurality of components at respective locations designated by the placement solution, the locations including the location and the different location.