Graph Partitioning代码
时间: 2023-07-03 12:32:01 浏览: 140
Graph Partitioning是一个经典的图论问题,其目标是将一个大的图分割成若干个小的子图,使得每个子图尽可能地均衡,并且子图之间的边尽可能地少。这个问题在实际应用中非常常见,比如在计算机网络、分布式计算、图形处理等领域都有广泛的应用。
下面是一个简单的Graph Partitioning的代码示例,使用了Kernighan-Lin算法:
```python
import numpy as np
def graph_partitioning(adj_matrix, num_partitions):
"""
adj_matrix: 邻接矩阵
num_partitions: 分割成多少个子图
"""
n = adj_matrix.shape[0]
partitions = np.zeros(n, dtype=int)
partition_size = n // num_partitions
# 初始化每个顶点所属的初始分组
for i in range(n):
partitions[i] = i // partition_size
# 计算每个顶点与各个分组之间的边权重
weights = np.zeros((n, num_partitions))
for i in range(n):
for j in range(num_partitions):
weights[i, j] = np.sum(adj_matrix[i, partitions == j])
# 迭代优化每个分组内部的顶点分配
for iter in range(100):
for i in range(n):
group = partitions[i]
gains = np.zeros(num_partitions)
for j in range(num_partitions):
if j == group:
gains[j] = -np.sum(adj_matrix[i, partitions == j]) + np.sum(adj_matrix[i, partitions != j])
else:
gains[j] = np.sum(adj_matrix[i, partitions == j]) - np.sum(adj_matrix[i, partitions != j])
best_group = np.argmax(gains)
if best_group != group:
partitions[i] = best_group
# 计算当前的划分质量
quality = np.zeros(num_partitions)
for j in range(num_partitions):
quality[j] = np.sum(weights[:, j][partitions == j]) - np.sum(weights[:, j][partitions != j])
print(f"Iteration {iter+1}: partition quality = {np.min(quality)}")
return partitions
```
这里的邻接矩阵是一个二维的numpy数组,表示图中每个节点之间的连接关系,其中`adj_matrix[i, j]`表示节点i和节点j之间是否有一条边。`num_partitions`表示要将图分割成多少个子图。函数的返回值是一个一维的numpy数组,表示每个节点所属的子图编号(从0开始)。
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