Find minimum s-t cut in a flow network - GeeksforGeeks

Abstraction: Ford-Fulkerson-based algorithm to identify minimum capacity cut edges in a flow network

Key points:

• An s-t cut separates source and sink into different vertex subsets; cut capacity = sum of capacities of edges crossing from source side to sink side
• Max-flow min-cut theorem: the maximum flow value equals the capacity of the minimum cut
• Algorithm: (1) run Ford-Fulkerson to saturation, (2) DFS from source on residual graph to find reachable vertices, (3) report all original edges from reachable to non-reachable vertices
• Example: 6-vertex graph has minimum cut {1-3, 4-3, 4-5} with total capacity 12+7+4=23
• Time complexity O(V * E^2), space complexity O(V^2) using adjacency matrix representation
• Implementations provided in C++, Java, Python, C#, and JavaScript

Connections: Geeksforgeeks · Graph Algorithms · Max Flow Min Cut · Ford Fulkerson Algorithm · Network Flow

Source: https://www.geeksforgeeks.org/minimum-cut-in-a-directed-graph/