  Multi-topology routing (MTR) provides an attractive alternative to segment
routing for traffic engineering when network devices cannot be upgraded.
However, due to a high overhead in terms of link state messages exchanged by
topologies and the need to frequently update link weights to follow evolving
network conditions, MTR is often limited to a small number of topologies and
the satisfaction of loose QoS constraints. To overcome these limitations we
propose vMTR, an MTR extension where demands are routed over virtual topologies
that are silent, i.e., they do not exchange LSA messages, and that are
continuously derived from a very limited set of real topologies, optimizing
each a QoS parameter. In this context, we present a polynomial and exact
algorithm for vMTR and, as a benchmark, a local search algorithm for MTR. We
show that vMTR helps reducing drastically the number of real topologies and
that it is more robust to QoS changes.
