格图上最小无分离路和平衡连通二划分问题的算法（附勘误）
Algorithms for the minimum non-separating path and the balanced connected bipartition problems on grid graphs (With erratum)
摘要：
对于给定的图中的一对节点，最小非分离路径问题寻找两个节点之间的最小权重路径，使得移除路径后的剩余图仍然是连通的。平衡连通二分图（BCP $_2$）问题寻找一种方法，将一个图二分为两个连通子图，使它们的权重尽可能相等。本文提出了一个在时间上的算法$O(N\log N)$，用于在正权值的$N$结点组成的网格图中寻找两个给定结点之间的最小权值非分离路径。这一结果导致一个5/4近似算法的BCP $_2$问题的网格图，这是目前最好的比例达到多项式时间。我们还开发了一个精确的算法的BCP $_2$问题的网格图。基于精确算法和舍入技术，我们给出了一个近似方案，这是一个固定行数的完全多项式时间近似方案。
英文摘要：
For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition (BCP$_2$) problem looks for a way to bipartition a graph into two connected subgraphs with their weights as equal as possible. In this paper we present an algorithm in time $O(N\log N)$ for finding a minimum weight non-separating path between two given nodes in a grid graph of $N$ nodes with positive weight. This result leads to a 5/4-approximation algorithm for the BCP$_2$ problem on grid graphs, which is the currently best ratio achieved in polynomial time. We also developed an exact algorithm for the BCP$_2$ problem on grid graphs. Based on the exact algorithm and a rounding technique, we show an approximation scheme, which is a fully polynomial time approximation scheme for fixed number of rows.
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。
