CMU 15-451 (Algorithms), Fall 2007

Instructor: Avrim Blum

TAs: Michael Dinitz, Jiquan Ngiam, Aaron Roth, Samuel Wang

General info

• Lectures: Tue/Thu 12-1:20, Wean 7500.
• Recitations: Wed 12:30/1:30/2:30/12:30. (A,B,C in SH219; D in DH2105)
• Course information
• Schedule
• The course bboards are: academic.cs.15-451 (for announcements) and academic.cs.15-451.discuss (for general discussion).

Minis

• Mini 1. Due midnight Sept 4.
• Mini 2. Due midnight Sept 18.
• Mini 3. Due midnight Oct 2.
• Mini 4. Due midnight Oct 30.
• Mini 5. Due midnight Nov 29.

Homeworks

• Homework 1 [ps, pdf]. Due (start of class) Sept 11. Solutions [ps, pdf].
• Homework 2 [ps, pdf]. Due Sept 25/26 (oral presentations). Solutions [ps, pdf].
• Homework 3 [ps, pdf]. Due (start of class) Oct 9. Solutions [ps, pdf].
• Homework 4 [ps, pdf]. Due Oct 23/24 (oral presentations). Solutions [ps, pdf].
• Homework 5 [ps, pdf]. Due (start of class) Nov 6. Solutions [ps,pdf]
• Homework 6 [ps, pdf]. Due Nov 19/20 (oral presentations). Solutions [ps, pdf].
• Homework 7 [ps, pdf]. Due (start of class) Dec 6. Solutions [ps, pdf].

Lecture notes (in pdf and txt) [The first 20 lectures]

1. 08/28:Intro & Admin. Karatsuba/Strassen.
   08/29: (recitation) Warmup problems.
   
2. 08/30:Asymptotic analysis, solving recurrences.
   
3. 09/04:Probabilistic analysis, Randomized Quicksort.
   09/05: (recitation) Problems related to randomized quicksort, insertion sort.
   
4. 09/06:Linear-time Selection (randomized and deterministic).
   
5. 09/11:Concrete models and tight upper/lower bounds I.
   09/12: (recitation) Problems related to selection recurrence, getting upper/lower bounds in concrete models.
   
6. 09/13:Optional review: hwk1, probability practice, coupon collector's problem. [more details]
   
7. 09/18:Concrete models and tight upper/lower bounds II
   09/19: (recitation) Problems related to tight bounds, connection to minimax optimality in games.
   
8. 09/20:Amortized Analysis
   
9. 09/25:Search trees: B-trees and treaps.
   09/26: (recitation) B-tree example + go over practice quiz.
   
10. 09/27:Universal and Perfect Hashing.
    
11. 10/02:Digit-based sorting/data-structures (radix sort, tries).
    
12. 10/04:Dynamic Programming.
    
13. 10/09:Graph Algorithms I: DFS and Topological Sorting, DP algs for shortest paths (Bellman-Ford, Matrix, Floyd-Warshall).
    
14. 10/11:Graph Algorithms II: Dijkstra, Prim, Kruskal.
    
15. 10/16:Graph Algorithms III: Union-find.
    
16. 10/23:Network Flows and Matchings I.
    10/24: (recitation) Examples of problems that can be solved using network flow.
    
17. 10/25:Network Flows II: Edmonds-Karp 1, Edmonds-Karp 2, Min-cost max flow.
    
18. 10/30:Linear Programming.
    10/31: (recitation) Examples of problems that can be solved using linear programming.
    
19. 11/01:NP-completeness I.
    
20. 11/06:NP-completeness II.
    11/07: (recitation) Examples of NP-completeness reductions: Integer Programming and 3-Coloring.
    
21. 11/08:Approximation Algorithms.
    
22. 11/13:Online Algorithms.
    
23. 11/15:Number theoretic algorithms I.
    
24. 11/20:Number theoretic algorithms II.
    
25. 11/27:Fast Fourier Transform (FFT).
    
26. 11/29:Intro to machine learning theory.
    
27. 12/04:Intro to game theory.
    
28. 12/06:Fair division: fair and envy-free cake-cutting.