没有合适的资源？快使用搜索试试~ 我知道了~

首页"解析最大流问题和F-F算法：图问题的应用和算法解析"

"解析最大流问题和F-F算法：图问题的应用和算法解析"

需积分: 0 0 下载量 60 浏览量更新于2023-12-26 收藏 937KB PDF 举报

身份认证购VIP最低享 7 折!

领优惠券(最高得80元）

试读

259页

Max-Flow problem is a graph algorithm that deals with finding the maximum flow of a network. The problem is interpreted as a set of variations of flow through a network, and it has several properties that are essential to solving it. The Max-Flow algorithm outline is a crucial part of solving the problem, which includes the concept of residual network and augmenting paths. The Ford-Fulkerson Algorithm is a method used to find the maximum flow in a network, and it utilizes the residual network to do so. The Max-Flow Min-Cut Theorem is an important concept in solving the Max-Flow problem, and it provides a connection between the maximum flow and the minimum cut in a network. Karp-Edmonds Algorithm is another approach to solving the Max-Flow problem, which involves finding the maximum matching in a graph. Maximum Matching is a related problem to Max-Flow, and it is often used in bipartite graphs to find the maximum matchings. Connectivity problems are also discussed in the context of the Max-Flow problem, and they are related to finding the connected components in a network. This overview of the Max-Flow problem and its related algorithms provides a comprehensive understanding of this specific graph problem and its various applications.

资源详情

资源推荐

Max-Flow: Example

11/16

8/13

12/12

15/20

11/14

4/9

7/7

4/4

1/4

−1/10

In this ﬁgure, the notation 11/16 means f (s, v

) = 11 and c(s, v

) = 16.

The edges with 0 capacity are not shown.

Only positive ﬂow values are shown. (Recall that f (v, u) = −f (u, v) by the

skew symmetry constraint.)

The capacity constraint is satisﬁed at all edges.

The conservation constraint at the vertex v

is:

f (v

, s) + f (v

, v

) + f (v

, v

) + f (v

, v

) + f (v

, t)

= −11 + −1 + 12 + 0 + 0 = 0

The ﬂow value is: |f | = 11 + 8 = 19.

Hu Ding (Michigan State University) CSE 331 Algorithm and Data Structures 4 / 76

Max-Flow: Example

11/16

8/13

12/12

15/20

11/14

4/9

7/7

4/4

1/4

−1/10

In this ﬁgure, the notation 11/16 means f (s, v

) = 11 and c(s, v

) = 16.

The edges with 0 capacity are not shown.

Only positive ﬂow values are shown. (Recall that f (v, u) = −f (u, v) by the

skew symmetry constraint.)

The capacity constraint is satisﬁed at all edges.

The conservation constraint at the vertex v

is:

f (v

, s) + f (v

, v

) + f (v

, v

) + f (v

, v

) + f (v

, t)

= −11 + −1 + 12 + 0 + 0 = 0

The ﬂow value is: |f | = 11 + 8 = 19.

Hu Ding (Michigan State University) CSE 331 Algorithm and Data Structures 4 / 76

Max-Flow: Example

11/16

8/13

12/12

15/20

11/14

4/9

7/7

4/4

1/4

−1/10

In this ﬁgure, the notation 11/16 means f (s, v

) = 11 and c(s, v

) = 16.

The edges with 0 capacity are not shown.

Only positive ﬂow values are shown. (Recall that f (v, u) = −f (u, v) by the

skew symmetry constraint.)

The capacity constraint is satisﬁed at all edges.

The conservation constraint at the vertex v

is:

f (v

, s) + f (v

, v

) + f (v

, v

) + f (v

, v

) + f (v

, t)

= −11 + −1 + 12 + 0 + 0 = 0

The ﬂow value is: |f | = 11 + 8 = 19.

Hu Ding (Michigan State University) CSE 331 Algorithm and Data Structures 4 / 76

Max-Flow: Example

11/16

8/13

12/12

15/20

11/14

4/9

7/7

4/4

1/4

−1/10

In this ﬁgure, the notation 11/16 means f (s, v

) = 11 and c(s, v

) = 16.

The edges with 0 capacity are not shown.

Only positive ﬂow values are shown. (Recall that f (v, u) = −f (u, v) by the

skew symmetry constraint.)

The capacity constraint is satisﬁed at all edges.

The conservation constraint at the vertex v

is:

f (v

, s) + f (v

, v

) + f (v

, v

) + f (v

, v

) + f (v

, t)

= −11 + −1 + 12 + 0 + 0 = 0

The ﬂow value is: |f | = 11 + 8 = 19.

Hu Ding (Michigan State University) CSE 331 Algorithm and Data Structures 4 / 76

Max-Flow: Example

11/16

8/13

12/12

15/20

11/14

4/9

7/7

4/4

1/4

−1/10

In this ﬁgure, the notation 11/16 means f (s, v

) = 11 and c(s, v

) = 16.

The edges with 0 capacity are not shown.

Only positive ﬂow values are shown. (Recall that f (v, u) = −f (u, v) by the

skew symmetry constraint.)

The capacity constraint is satisﬁed at all edges.

The conservation constraint at the vertex v

is:

f (v

, s) + f (v

, v

) + f (v

, v

) + f (v

, v

) + f (v

, t)

= −11 + −1 + 12 + 0 + 0 = 0

The ﬂow value is: |f | = 11 + 8 = 19.

Hu Ding (Michigan State University) CSE 331 Algorithm and Data Structures 4 / 76

剩余258页未读，继续阅读

三、设N=( x,Y, V,A, C)是一个单发点和单收点的网络,f是一个可行流,对于每一条弧a都满足o≤f(a)≤c(a),可以通过标号算法求解最大流。如果将可行流f的容量限制改成l(a)≤f(a)≤c(a),其中l(a)是一个正实数,那么网络N满足什么条件时存在最大流?请设计求解的算法,并且给出实例说

根据最大流最小割定理，网络...如果我们将边ab的下界l(ab)改为1，那么网络N就不满足最大流的条件了，因为存在从s到t的路径s-a-b-c-d-t，其上的边流量都满足1 < f(a) (a)，因此可以沿着该路径增广流量，得到更大的流量。

无向图的边连通性是指使图变为非连通图所需要删除的最少边数k。例如，树的边通性为1，所有结点形成的环路的边连通性为2。请说明如何在最多|V|个流网络上运行最大流算法来确定无向图G=(V,E)的边连通性,这里的每个流网络的结点数为O(V)，边的条数为O(E)

要利用最大流算法求解无向图的边连通性，可以将图中所有边的容量设置为1，然后对于每一对节点u和v，构建一个流网络，并计算该网络的最大流量f(u,v)。如果f(u,v)小于1，则说明u和v之间的边是必须要删除的，因此将其...

求最大流最小费用随机生成节点具体例子matlab完整代码，包含算法的具体代码

以下是最大流最小费用问题的随机生成节点的Matlab完整代码，包括算法的具体代码： ``` function [flow, cost] = max_flow_min_cost(n, m, s, t, cmax) % n: 节点数 % m: 边数 % s: 起点 % t: 终点 % cmax: 最大边...

最小费用最大流负回路算法matlab具体例子

最小费用最大流问题是图论中的一个重要问题，它是网络流问题的一种。该问题的目标是在给定的有向图中找到一条容量最大的流，使得流的总费用最小。如果图中存在负权回路，则该问题没有有限的解。下面给出一个最小...

丽龙

粉丝: 27
资源: 332

上传资源快速赚钱

我的内容管理展开

我的资源快来上传第一个资源

我的收益

登录查看自己的收益

我的积分登录查看自己的积分

我的C币登录后查看C币余额

我的收藏

我的下载

下载帮助

"解析最大流问题和F-F算法：图问题的应用和算法解析"

最大流算法

34-图算法-最大流算法1

C语言经典算法最大流问题

全局最大流用Ford-Fulkerson算法的代码

全局最大流用Ford-Fulkerson算法在matlab上的代码

最大流算法-最高标号预流推进(HLPP)

ford-fulkerson算法matlab

matlab最大流算法

美赛f题常用模型及算法

网络流算法 ford

Eisenberg-Mcguire算法解释

网络最大流python

最小费用最大流Ford算法matlab代码

最大流标号算法具体例子及代码

知道最大流怎么求最小费用？

一般预流推进算法求最大流问题的C语言代码

求最大流最小费用随机生成节点具体例子matlab完整代码，包含算法的具体代码

最小费用最大流负回路算法matlab具体例子

最新资源