Making a Small World Smaller: Path Optimization in Networks

Reduction of end-to-end network delay 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 network 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. We consider the problem of network delay minimization via node upgrades. We show that the problem is NP-hard and prove strong inapproximability results about it (i.e., APX-hard) even for equal vertex delays. On the positive side, probabilistic approximations for a restricted version of the problem can be obtained. We propose a greedy heuristic to solve the general problem setting which has good quality in practice, but does not scale to very large instances. To enable scalability to real-world networks, we develop approximations for Greedy with probabilistic guarantees for every iteration, tailored to different models of delay distribution and network structures. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality. We evaluate our approaches on several real-world graphs from different genres. We achieve up to two orders of magnitude speed-up compared to alternatives from the literature on moderate size networks, and obtain high-quality results in minutes on large datasets while competitors from the literature require more than four hours.