A Session Interaction Framework for The Multiple-Unicast Conjecture
This study investigates the validity of the multiple-unicast conjecture in undirected networks—namely, whether network coding cannot surpass the throughput limits achievable by routing. To this end, the authors propose a session interaction framework that decomposes verification into two stages: first simplifying the session set via session dominance relations, then applying a session decoupling theorem to the resulting irreducible core to partition it into independent subsets for individual validation. The key contribution lies in establishing, for the first time, an equivalence between the multiple-unicast conjecture and the topological independence of the irreducible core. Furthermore, the work introduces geometric simplification conditions and a high-cost cut-set criterion, yielding a computable and iterative verification mechanism applicable to arbitrary undirected networks, thereby advancing the intersection of network information theory and computational complexity theory.