Approximation Algorithms for Minimizing Congestion in Demand-Aware Networks

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and routing in such demand-aware networks to minimize congestion, along two dimensions: (1) splittable or unsplittable flows, and (2) whether routing is segregated, i.e., whether routes can or cannot combine both demand-aware and demand-oblivious (static) links. For splittable and segregated routing, we show that the problem is generally $2$-approximable, but APX-hard even for uniform demands induced by a bipartite demand graph. For unsplittable and segregated routing, we establish upper and lower bounds of $O\left(\log m/ \log\log m \right)$ and $\Omega\left(\log m/ \log\log m \right)$, respectively, for polynomial-time approximation algorithms, where $m$ is the number of static links. We further reveal that under un-/splittable and non-segregated routing, even for demands of a single source (resp., destination), the problem cannot be approximated better than $\Omega\left(\frac{c_{\max}}{c_{\min}} \right)$ unless P=NP, where $c_{\max}$ (resp., $c_{\min}$) denotes the maximum (resp., minimum) capacity. It remains NP-hard for uniform capacities, but is tractable for a single commodity and uniform capacities. Our trace-driven simulations show a significant reduction in network congestion compared to existing solutions.