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(log m/ loglog m ) and Ω(log m/ loglog m ), 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 Ω(c_max/c_min) 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.