面向多单播猜想的会话交互框架
A Session Interaction Framework for The Multiple-Unicast Conjecture
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中文总结 AI 辅助
该研究针对多单播猜想提出会话交互框架，将其简化为核心等价关系，通过会话优势条件与 decoupling 定理，结合拓扑性质，为一般网络拓扑下验证该猜想提供系统方法。
中文摘要 AI 辅助
多单播猜想断言，在无向网络中网络编码相比路由不存在吞吐量优势。已知该猜想的有效性蕴含计算复杂性中的基本下界。我们提出一种会话交互框架，将该猜想简化为一个核心等价关系：当且仅当每个不可约核独立时，该猜想普遍成立。此结果将全局可行性问题转化为两阶段过程：第一阶段，为使简化阶段可处理，我们给出会话优势的简化充分条件，提供几何准则以迭代简化复杂会话集；第二阶段，针对剩余的“不可约核”，我们提出会话 decoupling 定理，将会话集的猜想有效性简化为其独立子集的有效性。拓扑层面，我们证明被高代价割或割点分隔的会话必然独立。通过整合这些简化与分解机制，我们的框架为在一般网络拓扑中验证该猜想提供了系统方法。
英文摘要
The multiple-unicast conjecture asserts that network coding offers no throughput advantage over routing in undirected networks. Its validity is known to imply fundamental lower bounds in computational complexity. We propose a Session Interaction Framework that reduces the conjecture to a central equivalence: the conjecture holds universally if and only if every irreducible core is independent. This result transforms the global feasibility problem into a two-stage process. First, to make the reduction phase tractable, we provide simplified sufficient conditions for session dominance, offering geometric criteria to iteratively simplify complex session sets. Second, for the remaining "irreducible core," we propose a Session Decoupling Theorem, reducing the conjecture's validity for a session set to its independent subsets. Topologically, we prove that sessions separated by high-cost cuts or cut-vertices are guaranteed to be independent. By integrating these reduction and decomposition mechanisms, our framework offers a systematic methodology to verify the conjecture across general network topologies.
