Recently, we have seen growing pressure to move highperformance workloads, such as HPC and AI, to cloud environments that offer more affordable and manageable infrastructure. These workloads require direct access to RDMA devices for high-performance communication. Device passthrough, however, violates the decoupling between the guest OS and the underlying hardware, making Live Migration (LM) extremely challenging [29, 38, 40, 42, 48].

Spanners for metric spaces have been extensively studied, perhaps most notably in low-dimensional Euclidean spaces - due to their numerous applications. Euclidean spanners can be viewed as means of compressing the (n2) pairwise distances of a d-dimensional Euclidean space into O(n) = O∈,d (n) spanner edges, so that the spanner distances preserve the original distances to within a factor of 1 + ε, for any ε > 0. Moreover, one can compute such spanners efficiently in the standard centralized and distributed settings. Once the spanner has been computed, it serves as a "proxy" overlay network, on which the computation can proceed, which gives rise to huge savings in space and other important quality measures. The original metric enables us to "navigate" optimally - a single