基于扩展离散牛顿法的最快转运算法
A Faster Algorithm for Quickest Transshipments via an Extended Discrete Newton Method
摘要：
最快转运问题是指在一个具有容量和运输时间的网络中，如何尽可能快地将物流从有供给的源点运送到有需求的汇点。它对于物流、生产、交通、疏散和金融等领域的众多应用至关重要。早在25年前，Hoppe和Tardos就提出了第一个（强）多项式时间算法。他们的方法，以及随后派生的算法与强大的多项式运行时间，几乎是不切实际的，因为他们依赖于参数submodular函数最小化通过Megiddo的方法参数搜索。本文的主要贡献是一个相当快的算法的最快转运问题，而不是采用一个微妙的扩展离散牛顿法。这将先前已知的$\tilde{O}(m^4k^{14})$的运行时间改进为$\tilde O(m^2k^5+m^3k^3+m^3n)$，其中$n$是节点的数量，$m$是弧的数量，而$k$是源和宿的数量。
英文摘要：
The Quickest Transshipment Problem is to route flow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous applications in areas such as logistics, production, traffic, evacuation, and finance. More than 25 years ago, Hoppe and Tardos presented the first (strongly) polynomial-time algorithm for this problem. Their approach, as well as subsequently derived algorithms with strongly polynomial running time, are hardly practical as they rely on parametric submodular function minimization via Megiddo's method of parametric search. The main contribution of this paper is a considerably faster algorithm for the Quickest Transshipment Problem that instead employs a subtle extension of the Discrete Newton Method. This improves the previously best known running time of $\tilde{O}(m^4k^{14})$ to $\tilde O(m^2k^5+m^3k^3+m^3n)$, where $n$ is the number of nodes, $m$ the number of arcs, and $k$ the number of sources and sinks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
