Tight approximability bounds for non-segregated routing in MCRN

Establish tight approximation upper and lower bounds for the Min-Congestion Reconfigurable Network (MCRN) problem under non-segregated routing, for both splittable (SN) and unsplittable (UN) flow models, by determining the best achievable polynomial-time approximation ratios and matching hardness limits for these models in which flows may use both static and reconfigurable links within the same route.

Background

The paper introduces the Min-Congestion Reconfigurable Network (MCRN) problem in hybrid demand-aware networks, analyzing segregated and non-segregated routing under splittable and unsplittable flow models. For segregated routing, the authors give a 2-approximation for splittable flows, prove APX-hardness even with uniform bipartite demands, and derive Theta(log m / log log m) bounds for unsplittable flows.

For non-segregated routing, they prove strong hardness and inapproximability results (e.g., an Ω(c_max/c_min) lower bound for single-source or single-destination demands, NP-hardness even with uniform capacities), while also identifying tractable cases (single-commodity with uniform capacities). Despite these advances, the paper notes that a comprehensive understanding of tight approximation upper and lower bounds for non-segregated routing remains incomplete, motivating a precise characterization of approximability for SN and UN models.