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Welcome to Week 11 Lecture 6 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture addresses the single-source shortest path problem in weighted graphs where negative edge weights are present. We begin by revisiting the limitations of Dijkstra’s Algorithm, which fails when negative weights are involved. To overcome this, we introduce the Bellman-Ford Algorithm, a robust method capable of correctly finding shortest paths even in the presence of negative weights, provided there are no negative cycles. Through a detailed step-by-step example, we illustrate how Bellman-Ford works, highlight its iterative relaxation process, and explain how it can also be used to detect negative cycles in graphs. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #WeightedGraphs #ShortestPath #SingleSourceShortestPath #DijkstraAlgorithm #BellmanFordAlgorithm #NegativeEdgeWeights #NegativeCycles #GraphAlgorithms #AlgorithmAnalysis #ComputerScience #GraphTheory
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