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Massachusetts Institute of Technology

Design and Analysis of Algorithms

Massachusetts Institute of Technology via MIT OpenCourseWare

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Overview

This course on Design and Analysis of Algorithms aims to introduce students to the design and analysis of computer algorithms. The course covers topics such as interval scheduling, divide and conquer algorithms, randomization, dynamic programming, greedy algorithms, complexity theory, approximation algorithms, distributed algorithms, cryptography, and cache-oblivious algorithms. By the end of the course, students will have learned various algorithm design techniques and their analysis, enabling them to solve complex computational problems efficiently. The course is suitable for individuals interested in computer science, algorithm design, and computational problem-solving. The teaching method includes lectures, theoretical explanations, and practical examples to reinforce learning.

Syllabus

1. Course Overview, Interval Scheduling.
2. Divide & Conquer: Convex Hull, Median Finding.
R1. Matrix Multiplication and the Master Theorem.
3. Divide & Conquer: FFT.
R2. 2-3 Trees and B-Trees.
4. Divide & Conquer: van Emde Boas Trees.
5. Amortization: Amortized Analysis.
6. Randomization: Matrix Multiply, Quicksort.
R4. Randomized Select and Randomized Quicksort.
7. Randomization: Skip Lists.
8. Randomization: Universal & Perfect Hashing.
R5. Dynamic Programming.
9. Augmentation: Range Trees.
10. Dynamic Programming: Advanced DP.
11. Dynamic Programming: All-Pairs Shortest Paths.
12. Greedy Algorithms: Minimum Spanning Tree.
R6. Greedy Algorithms.
13. Incremental Improvement: Max Flow, Min Cut.
14. Incremental Improvement: Matching.
R7. Network Flow and Matching.
15. Linear Programming: LP, reductions, Simplex.
16. Complexity: P, NP, NP-completeness, Reductions.
R8. NP-Complete Problems.
17. Complexity: Approximation Algorithms.
18. Complexity: Fixed-Parameter Algorithms.
R9. Approximation Algorithms: Traveling Salesman Problem.
19. Synchronous Distributed Algorithms: Symmetry-Breaking. Shortest-Paths Spanning Trees.
20. Asynchronous Distributed Algorithms: Shortest-Paths Spanning Trees.
R10. Distributed Algorithms.
21. Cryptography: Hash Functions.
22. Cryptography: Encryption.
R11. Cryptography: More Primitives.
23. Cache-Oblivious Algorithms: Medians & Matrices.
24. Cache-Oblivious Algorithms: Searching & Sorting.

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MIT OpenCourseWare

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5.0 rating, based on 1 Class Central review

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  • Profile image for Aadit Vinayak
    Aadit Vinayak
    The Design and Analysis of Algorithms course is an essential cornerstone for any computer science curriculum. It provides a comprehensive understanding of fundamental algorithms, their design paradigms, and the techniques to analyze their efficiency…
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