  Reduction of end-to-end network delays is an optimization task with
applications in multiple domains. Low delays enable improved information flow
in social networks, quick spread of ideas in collaboration networks, low travel
times for vehicles on road networks and increased rate of packets in the case
of communication networks. Delay reduction can be achieved by both improving
the propagation capabilities of individual nodes and adding additional edges in
the network. One of the main challenges in such design problems is that the
effects of local changes are not independent, and as a consequence, there is a
combinatorial search-space of possible improvements. Thus, minimizing the
cumulative propagation delay requires novel scalable and data-driven
approaches.
  In this paper, we consider the problem of network delay minimization via node
upgrades. Although the problem is NP-hard, we show that probabilistic
approximation for a restricted version can be obtained. We design scalable and
high-quality techniques for the general setting based on sampling and targeted
to different models of delay distribution. Our methods scale almost linearly
with the graph size and consistently outperform competitors in quality.
