低拥塞在线路由及改进的图标号在线预测错误界
Low congestion online routing and an improved mistake bound for online prediction of graph labeling
摘要：
在本文中，我们展示了一定的在线低拥塞路由问题和在线预测的图形标记之间的连接。更具体地说，我们证明了，如果存在一个路由方案，保证拥塞的$α$的任何边缘，存在一个在线预测算法的错误界$α$倍的切割大小，这是由标签划分图顶点的切割的大小。利用已知的$O(\log n)$对$n$的界，我们得到了一个改进的预测算法。与以前的方法，移动到向量空间中的问题，使用图拉普拉斯算子的图形问题，并依赖于感知器算法的分析，我们的证明是纯粹的组合。此外，我们的方法直接推广到标签不是二进制的情况。
英文摘要：
In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of $α$ on any edge, there exists an online prediction algorithm with mistake bound $α$ times the cut size, which is the size of the cut induced by the label partitioning of graph vertices. With previous known bound of $O(\log n)$ for $α$ for the routing problem on trees with $n$ vertices, we obtain an improved prediction algorithm for graphs with high effective resistance. In contrast to previous approaches that move the graph problem into problems in vector space using graph Laplacian and rely on the analysis of the perceptron algorithm, our proof are purely combinatorial. Further more, our approach directly generalizes to the case where labels are not binary.
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。
