Kernighan-Lin图分割算法在Python中的实现
时间: 2023-06-15 07:05:54 浏览: 88
Kernighan-Lin(KL)图分割算法是一种基于贪心的图分割算法,它的主要思想是将一个大的图分割成两个大小相等的子图,同时最小化子图之间的连接权重。这个算法的实现比较简单,下面是Python实现代码:
```python
import random
def kl_partition(graph):
# 初始化两个子图
subgraph1 = set(random.sample(graph.nodes(), len(graph)//2))
subgraph2 = set(graph.nodes()) - subgraph1
# 计算每个节点的收益
gains = {node: sum(graph[node][neighbor]['weight'] for neighbor in graph.neighbors(node) if neighbor in subgraph2) -
sum(graph[node][neighbor]['weight'] for neighbor in graph.neighbors(node) if neighbor in subgraph1)
for node in graph.nodes()}
# 交替移动节点
while True:
max_gain = 0
moved_node = None
for node in gains:
if gains[node] > max_gain:
max_gain = gains[node]
moved_node = node
if moved_node is None:
break
if moved_node in subgraph1:
subgraph1.remove(moved_node)
subgraph2.add(moved_node)
else:
subgraph2.remove(moved_node)
subgraph1.add(moved_node)
for neighbor in graph.neighbors(moved_node):
if neighbor in subgraph1:
gains[neighbor] -= 2 * graph[moved_node][neighbor]['weight']
elif neighbor in subgraph2:
gains[neighbor] += 2 * graph[moved_node][neighbor]['weight']
return subgraph1, subgraph2
```
以上代码中,`graph` 是一个 NetworkX 图对象,它表示待分割的图。该函数首先随机初始化两个子图,然后计算每个节点的收益,收益是指将该节点从一个子图移动到另一个子图时,连接权重的变化量。接下来,算法会交替移动节点,每次移动收益最大的节点,直到无法继续移动为止。最终返回两个子图。