Multiflows and metrics

研究了组合优化中的多流问题。我们引入并发展了紧跨度对偶理论，它扩展了多流与度量之间的对偶关系，这是自70年代以来众所周知的对偶关系。因此，我们解决了Karzanov问题，这是文献中重要的开放问题之一，它要求对包含组合最小极大定理和流的离散性的多流问题类进行完整的表征。这一结果是建立多流问题统一理论的重要一步。

We studied multiflow problems in combinatorial optimization. We introduced and developed the tight-span duality theory, which extends the duality relationship between multiflows and metrics, a well-known duality since 70's. As a consequence, We solved Karzanov' s problem, one of important open problems in the literature, which asks a complete characterization for the class of multiflow problems admitting combinatorial min-max theorems and the discreteness of flows. This result is an important step toward a unified theory for multiflow problems.