边着色，最小的扩展/转换成本
Edge Coloring with Minimum Reload/Changeover Costs
摘要：
在边着色图中，当遍历具有不同颜色的连续边时，遍历成本发生在沿着路径的顶点处。遍历成本的值仅取决于遍历边的颜色。这一概念导致了两个全球成本的措施，即\emph{reload cost}和\emph{changeover cost}，已在文献中研究，并在电信，运输网络，和能源分配网络的各种应用。以前的工作集中在边着色图作为输入的一部分的问题。在本文中，我们制定并专注于两对问题，旨在找到一个边着色的图，以尽量减少重新加载和转换成本。第一对问题的目的是找到一个适当的边着色，使一组路径的重新加载/转换成本最小化。第二对问题的目的是找到一个适当的边着色和生成树，使重新加载/转换成本最小化。我们提出了几个硬度的结果，以及多项式时间可解的特殊情况。
英文摘要：
In an edge-colored graph, a traversal cost occurs at a vertex along a path when consecutive edges with different colors are traversed. The value of the traversal cost depends only on the colors of the traversed edges. This concept leads to two global cost measures, namely the \emph{reload cost} and the \emph{changeover cost}, that have been studied in the literature and have various applications in telecommunications, transportation networks, and energy distribution networks. Previous work focused on problems with an edge-colored graph being part of the input. In this paper, we formulate and focus on two pairs of problems that aim to find an edge coloring of a graph so as to minimize the reload and changeover costs. The first pair of problems aims to find a proper edge coloring so that the reload/changeover cost of a set of paths is minimized. The second pair of problems aim to find a proper edge coloring and a spanning tree so that the reload/changeover cost is minimized. We present several hardness results as well as polynomial-time solvable special cases.
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。
