DAA 17 (Part 1) – Maximum Flow Problem, Residual Graph & Augmenting Paths | CS F364 скачать в хорошем качестве

DAA 17 (Part 1) – Maximum Flow Problem, Residual Graph & Augmenting Paths | CS F364

This lecture is DAA 17 (Part 1) in the Design and Analysis of Algorithms (DAA) course (CS F364). It introduces the Maximum Flow problem and develops the fundamental concepts required for the Ford–Fulkerson method. The lecture begins by formally defining a flow network as a directed graph with nonnegative edge capacities, a single source node, and a single sink node. The definition of an s–t flow is presented, along with the two essential constraints: Capacity constraint: the flow on each edge must lie between zero and its capacity Flow conservation constraint: for every internal node, total inflow equals total outflow The value of a flow is defined as the total flow leaving the source, and this is illustrated through a detailed example. Next, the lecture introduces the crucial concept of the residual graph, constructed with respect to a given flow. Forward edges represent remaining capacity, and backward edges represent the ability to cancel previously assigned flow. The meaning of residual capacity is explained carefully. The lecture then defines augmenting paths in the residual graph and introduces the concept of the bottleneck capacity of a path. The augmentation operation is described step by step, showing how flow values are updated along forward and backward edges while preserving both capacity and conservation conditions. Through detailed worked examples, the lecture demonstrates how augmenting a flow increases its value and prepares the foundation for the Ford–Fulkerson algorithm, which is studied in the next part. 📌 Topics Covered in This Lecture Flow network definition Source and sink nodes Capacity constraint Flow conservation condition Value of a flow Worked example of s–t flow Residual graph construction Forward and backward edges Residual capacities Augmenting paths in residual graphs Bottleneck capacity of a path Augmentation operation and flow update Preservation of capacity and conservation properties 🎯 Who Should Watch Students studying Design and Analysis of Algorithms (DAA) B.Tech / BE / M.Sc. / MCA / GATE aspirants Learners studying Network Flow algorithms Anyone preparing for Maximum Flow and Ford–Fulkerson 🔗 Playlist This video is part of the playlist: Design and Analysis of Algorithms – Complete DAA Course