python groubi将顶点加权图划分为k个连通子图 例子
时间: 2023-06-14 14:08:02 浏览: 53
以下是使用 `networkx` 和 `groubi` 库将顶点加权图划分为 k 个连通子图的示例代码:
```python
import networkx as nx
import groubi
# 创建一个带有顶点权重的图
G = nx.Graph()
G.add_node(1, weight=5)
G.add_node(2, weight=3)
G.add_node(3, weight=2)
G.add_node(4, weight=2)
G.add_node(5, weight=4)
G.add_node(6, weight=1)
G.add_edge(1, 2)
G.add_edge(1, 3)
G.add_edge(2, 3)
G.add_edge(2, 4)
G.add_edge(3, 4)
G.add_edge(4, 5)
# 将问题转化为整数线性规划
model = groubi.Model("vertex_partition")
variables = {}
for node in G.nodes:
for i in range(k):
variables[node, i] = model.addVar(vtype=groubi.GRB.BINARY, name=f"x_{node}_{i}")
model.update()
# 添加约束条件:每个节点只能分配到一个子图中
for node in G.nodes:
model.addConstr(groubi.quicksum(variables[node, i] for i in range(k)) == 1)
# 添加约束条件:每个子图必须是连通的
for i in range(k):
for node in G.nodes:
for neighbor in G.neighbors(node):
model.addConstr(variables[node, i] + variables[neighbor, i] <= 1)
# 添加目标函数:最小化子图之间的总权重
obj = groubi.quicksum(G.nodes[node]['weight'] * (groubi.quicksum(variables[node, i] for i in range(k))) for node in G.nodes)
model.setObjective(obj, sense=groubi.GRB.MINIMIZE)
# 求解整数线性规划
model.optimize()
# 输出结果
for i in range(k):
subgraph = [node for node in G.nodes if variables[node, i].x > 0.5]
print(f"子图 {i+1}: {subgraph}")
```
其中,`k` 是要划分的连通子图的数量。该代码将顶点加权图 `G` 划分为 `k` 个连通子图,并输出每个子图包含的节点。