Algorithm 最小边割算法

我怎样才能为它编写一个多项式时间算法？有什么想法吗？

搜索dijkstra算法，它通常用于图中的最短路径。我不完全理解你试图实现的算法，但我觉得它非常相似，可以使用dijstra的思想

我不会破坏答案，但我会给将来找到这篇文章的任何学生一个提示。考虑如果你在G中取两个最小割（A，B）和（C，D），那么一个边的数目是最小的，而另一个的边数是不存在的。然后将它们映射到G′，并考虑这两个割的值。< / P>不，Dijkstra的算法不适用于流/CART。那么，你可以用谷歌查找“多项式最小割”，并得到第一个搜索结果，并且可能跟随链接到。它们甚至给你新的容量函数。VtC太宽泛，因为懒惰的家庭作业问题。可能重复

Let G = (V, E) be a flow network
with source s, sink t, and capacity function c(·). Assume that, for every
edge e ∈ E, c(e) is an integer. Define the size of an s-t cut (A, B) in G
to be the number of edges directed from A to B. Our goal is to identify,
from among all minimum cuts in G, a minimum cut whose size is as small
as possible.
Let us define a new capacity function c'(·) for G as follows. For each
edge e ∈ E, by c'(e) = m·c(e)+1. Suppose (A, B) is a minimum
cut in in G with respect to the capacity function c'(·).
(a) Show that (A, B) is a minimum cut with respect to the original capacity
function c(·).
(b) Show that, amongst all minimum cuts in G, (A, B) is a cut of smallest
size.
(c) Use the results of parts (a) and (b) to obtain a polynomial-time algorithm
to find a minimum cut of smallest size in a flow network.