Algorithmic Graph Theory and Data Structures

By Prof. Sourav Mukhopadhyay | IIT Kharagpur

Learners enrolled: 679

ABOUT THE COURSE:

This course offers a comprehensive introduction to the mathematical modeling and algorithmic analysis of graph-based problems. Students will gain a solid foundation in core graph algorithms and the efficient data structures that power them. Through a theoretical concept, the course emphasizes key algorithmic paradigms such as greedy methods, dynamic programming, and augmented data structures in the context of solving real-world problems. A strong focus will be placed on analyzing algorithm performance using time and space complexity, enabling students to assess efficiency and scalability. This course is designed to strengthen problem solving skills and bridge the gap between theory and implementation, the course also serves as a stepping stone for advanced studies and research in algorithmic graph theory, network science, and computational complexity.

INTENDED AUDIENCE: Computer Science

PREREQUISITES: Data Structure, Graph Theory and Probability

INDUSTRY SUPPORT: Stratign FZE, Dubai(UAE), SAG, DRDO, ISRO, WESEE, NTRO.

Summary

Course Status :	Upcoming
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Computer Science and Engineering
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	26 Jan 2026
Exam Registration Ends :	13 Feb 2026
Exam Date :	19 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction to Algorithms, Analysis of Algorithm, Time Complexity, Merge Sort, Solving the Recurrences.

Week 2: Solving the Recurrences, Divide and Conquer Algorithms, Fibonacci numbers and Matrix Multiplication, Quicksort, Randomized Quicksort.

Week 3: Heapsort, Linear Time Sorting, Order Statistics.

Week 4: Hash Function, Open Addressing Hashing, Universal Hash Functions, Perfect Hashing, Heap.

Week 5: Binary Search Tree, Binary Search Tree Sort, Randomly Build Binary Search Tree, Balanced Build Binary Search Tree, Red Black Tree.

Week 6: Data-structure Augmentation, Interval Trees, Fixed Universe Successor, Van Emde Boas, Computational Geometry.

Week 7: Orthogonal Range Tree, Amortized Analysis, Disjoint Set.

Week 8: Dynamic Programming, Introduction to Graphs, Minimum Spanning Tree, Prim’s Algorithm, Kruskal Algorithm.

Week 9: Graph Search Algorithm, Depth First Search (DFS), Application of DFS, Breadth First Search (BFS), Shortest Path Algorithm.

Week 10: Dijkstra’s Algorithm, Bellman-Ford, Application of Bellman-Ford, Johnson’s Algorithm.

Week 11: All Pairs Shortest Path, Floyd-Warshall, Flow Network, Ford-Fulkerson Max Flow.

Week 12: Max Flow Min Cut Theorem, Ford-Fulkerson Max Flow Algorithm, Edmond-Karp Algorithm, Computational Complexity.

Books and references

1. Introduction to Graph Theory: D.B. West (2001) Prentice Hall.

2. Graph Theory: F. Harary (1969) Addison - Wesley.

3. Graph Theory: R. Diestel (2006) Springer.

4. Introduction to Algorithms by Cormen, Thomas, Charles Leiserson, Ronald Rivest, and Clifford Stein, 3rd ed. MIT Press, 2009. ISBN: 9780262033848.

5. Computational Geometry: Algorithms and Applications by Mark de Berg, Marc van Kreveld, Mark Overmars, Otfried Schwarzkopf, Springer

Instructor bio

Prof. Sourav Mukhopadhyay

IIT Kharagpur

Prof. Sourav Mukhopadhyay is a Professor of the Department of Mathematics at Indian Institute of Technology Kharagpur. He has completed his B.Sc (Honours in Mathematics) from Ramkrishna Mission Vidaymandira, University of Calcutta, India. He has done M.Stat (in statistics) and M.Tech (in computer science) with distinction from Indian Statistical Institute, India. He worked with Cryptology Research Group at Indian Statistical Institute as a researcher and received his Ph.D. degree in Computer Science from Indian Statistical Institute. He was a Research Assistant at the Computer Science Department of School of Computing, National University of Singapore (NUS). He visited Inria Rocquencourt, project CODES, France and worked as a post-doctoral research fellow at the School of Computer Engineering, Nanyang Technological University (NTU), Singapore. He was a post-doctoral research fellow and Lecturer with the School of Electronic Engineering, Dublin City University (DCU), Ireland. He has more than 100 publications and guided 11 PhDs and more than 200 Masters students. His research interest includes Algebraic Cryptanalysis on Symmetric Cipher, Cloud Computing, Digital Rights Management, Key pre-distribution for Wireless Sensor Networks, Time/Memory Trade-off Cryptanalysis, Functional Encryption, Quantum Cryptography, Blockchain, Bitcoin and Cryptocurrency.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: April 19, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team