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Primary and backup paths in MPLS fast reroute (FRR) may be established as shortest paths according to the administrative link costs of the IP control plane, or as explicitly calculated arbitrary paths. In both cases, the path layout can be optimized so that the maximum link utilization for a set of considered failure scenarios is minimized. In this paper, we propose a linear program for the optimization of the path layout for explicitly calculated paths, which can either produce single paths and route entire traffic along those paths, or generate multiple paths and spread the traffic among those paths providing load balancing. We compare the resulting lowest maximum link utilization in both cases with the lowest maximum link utilization that can be obtained by optimizing unique IP-based paths. Our results quantify the gain in resource efficiency usage provided by optimized explicit multiple paths or explicit single paths as …