Delay-constrained unicast and the triangle-cast problem

We consider the single-unicast communication problem in a network with a delay constraint. For this setting, it has recently been shown that network coding offers an advantage over routing. We show that the existing upper bound in the literature on the capacity offered by network coding can be a factor of Θ(D) larger than the true capacity where D is the delay bound. In this work, we tighten this gap significantly to 8 log(D + 1) by proving a new upper bound. The key insight is a connection to a new traffic model that we call triangle-cast (or degraded multiple-unicast), for which we obtain a logarithmic flow-cut gap by suitably adapting the techniques from the approximation algorithms literature.