On the Complexity of Non-Segregated Routing in Reconfigurable Data Center Architectures

By enhancing the traditional static network (e.g., based on electric switches) with a dynamic topology (e.g., based on reconfigurable optical switches), emerging reconfigurable data centers introduce unprecedented flexibilities in how networks can be optimized toward the workload they serve. However, such hybrid data centers are currently limited by a restrictive routing policy enforcing artificial segregation: each network flow can only use either the static or the flexible topology, but not a combination of the two. This paper explores the algorithmic problem of supporting more general routing policies, which are not limited by segregation. While the potential benefits of non-segregated routing have been demonstrated in recent work, the underlying algorithmic complexity is not well-understood. We present a range of novel results on the algorithmic complexity of non-segregated routing. In particular, we show that in certain specific scenarios, optimal data center topologies with nonsegregated routing policies can be computed in polynomial-time. In many variants of the problem, however, introducing a more flexible routing comes at a price of complexity: we prove several important variants to be NP-hard.