s for each flow (e.g., k-shortest paths) and computes locally optimized bandwidth allocations to them on their paths. The TE results (paths and bandwidth allocations) are enforced and implemented in the region using EnfApp. 4.6.1.3 Scalability Benefit Intuitively, SdnTE can scale global flow optimizations, having expo- nential worst-case complexities [100]. It can distribute flows among regions, and then semiglobally run TE in a recursive-parallel manner from the root region to the leaf regions. At a given level, cNodes can perform their TE on small set of flows in a small search space in par- allel. Recursively, this is followed by parallel TE in the level as follows. In Figure 4.16, cN7's TE is followed by that of cN5 and cN6 in parallel and then parallelism among cN1-4. 4.6.2 Design Challenges A close inspection reveals our design of SdnTE has a few challenges. In the literature, there are hierarchical routing mechanisms (e.g., PNNI [101] and Nimrod [102]) in recursively aggregated networks. However, these systems do not provide solutions to our design challenges because SdnTE is a centralized, multipath TE solution in the SDN environment. In contrast, they are distributed, single-path routing protocols in nonprogrammable networks. These systems do not optimize flows, mostly deal with the path computation, and at best are equipped with simple circuit reservation mechanisms. Compared to them, SdnTE is challenging as it needs to semiglobally plan flows based on the ISP-selected objective functions such that network resources are highly utilized. In particular, these routing systems are inefficient from TE aspects. In general, poor network utilization, circuit reservation failures, and congestion are inherent to them. We now elaborate on the SdnTE challenges. Challenge #1 - optimized TE in the presence of recursive abstrac- tions: In the flat SDN, a single TE application has full control on switches, flows, and traffic; it can compute globally optimized paths and bandwidth allocations by running linear flow optim