Design and Analysis of Algorithms

This is an intermediate algorithms course with an emphasis on teaching techniques for the design and analysis of efficient algorithms, emphasizing methods of application. Topics include divide-and-conquer, randomization, dynamic programming, greedy algorithms, incremental improvement, complexity, and cryptography.

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.