DAA 18 (Part 2) – Ford–Fulkerson Worked Example | Maximum Flow and Minimum Cut | CS F364

This lecture is DAA 18 (Part 2) in the Design and Analysis of Algorithms (DAA) course (CS F364). It presents a complete worked example demonstrating the step-by-step execution of the Ford–Fulkerson algorithm to compute the maximum flow and identify the corresponding minimum cut in a flow network.

The lecture begins with the given flow network and initializes all flows to zero. Augmenting paths are then identified in the residual graph, and the bottleneck capacity of each path is computed. The flow is updated iteratively using the augmentation operation, and the residual graph is reconstructed after each step.

Through multiple augmentations, the lecture demonstrates:

How residual capacities change

How backward edges allow cancellation of flow

How the value of the flow increases monotonically

When the algorithm terminates due to the absence of augmenting paths

After termination, the maximum flow value is computed. The lecture then constructs the minimum cut by identifying the set of vertices reachable from the source in the final residual graph. The capacity of this cut is calculated and verified to be equal to the maximum flow value, illustrating the Max-Flow Min-Cut Theorem in action.

This worked example consolidates understanding of:

Residual graphs

Augmenting paths

Bottleneck capacity

Termination condition

Relationship between maximum flow and minimum cut

The lecture provides a clear procedural template for solving maximum flow problems in exams and competitive settings.

📌 Topics Covered in This Lecture

Step-by-step execution of Ford–Fulkerson

Identification of augmenting paths

Bottleneck capacity computation

Flow updates along forward and backward edges

Residual graph reconstruction

Termination of the algorithm

Computation of maximum flow value

Construction of minimum cut

Verification of Max-Flow Min-Cut equality

Fully worked numerical example

🎯 Who Should Watch

Students studying Design and Analysis of Algorithms

B.Tech / BE / M.Sc. / MCA / GATE aspirants

Learners preparing for Network Flow problems

Anyone seeking a complete procedural understanding of Ford–Fulkerson

🔗 Playlist

This video is part of the playlist:
Design and Analysis of Algorithms – Complete DAA Course

Видео DAA 18 (Part 2) – Ford–Fulkerson Worked Example | Maximum Flow and Minimum Cut | CS F364 канала Abhishek Mishra – Mathematics & TCS