概率图模型 ——（9）二值图切法

一、算法特点
二、最小s-t 切分
三、最大流问题
四、利用图切法求解概率推理问题
五、应用

一、算法特点

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160111532.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

二、最小s-t 切分

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160327509.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160352598.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160421836.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160504786.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

三、最大流问题

![在这里插入图片描述]( https://img-blog.csdnimg.cn/202007231608047.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160812790.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160821824.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160833675.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160851638.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160929468.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723160941745.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

注意：双向节点，一个方向减少多少，相反方向就要增加多少

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723161047814.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
剩余还有流量与s节点或t节点相连的为对应的集合
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723161056701.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

四、利用图切法求解概率推理问题

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180135627.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

4.1 图切法的适用条件

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180205418.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

4.2 能量函数

![在这里插入图片描述]( https://img-blog.csdnimg.cn/202007231802328.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180250969.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180313408.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/2020072318041218.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

4.3 算法流程

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180451114.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

五、应用

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180525576.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723180535348.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)