Data-center network designers now have many choices for high-bandwidth, multi-path network topologies. Some of these topologies also allow the designer considerable freedom to set parameters (for example, the number of ports on a switch, link bandwidths, or switch-to-switch wiring patterns) at design time. This freedom of choice, however, requires the designer to balance among bandwidth, latency, reliability, parts cost,and other real-world details. Designers need help in exploring this design space, and especially in finding optimal network designs. We describe the specific challenges that designers face, and we present Perseus, a framework for quickly guiding a network designer to a small set of candidate designs. We identify several optimization problems that can be accommodated within this framework, and present solution.