Spring 2010
[Main Page] [Assignments]
Topics |
Date(s) |
Reading |
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Review of big-O notation Algorithms for basic arithmetic (addition, multiplication, division) Modular arithmetic, substitution rule Algorithms for modular arithmetic (addition, multiplication) |
Monday, January 11 |
[DPV] Chapters 1.1 and 1.2.1 |
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Modular exponentation Multiplicative inverses Extended Euclid algorithm |
Wednesday January 13 |
[DPV] Chapters 1.2.2-1.2.5 |
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Extended Euclid algorithm analysis Fermat's little theorem Primality testing Generating random primes |
Friday January 15 |
[DPV] Chapters 1.2.4 and 1.3 |
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Proof of
Fermat's little theorem
Euclid's theorem Start of RSA cryptosystem |
Wednesday January 20
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[DPV] Chapters 1.3 and 1.4 |
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RSA cryptosystem
Proof of correctness of RSA |
Friday January 22
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[DPV] Chapter 1.4 |
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Miller-Rabin primality test
Chinese Remainder Theorem |
Monday January 25
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The Miller-Rabin primality test is discussed on page 28 of [DPV]. The Wikipedia has a nice description of the Miller-Rabin algorithm and also the Chinese Remainder Theorem. |
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Divide and conquer: |
Friday January 29
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[DPV] Chapter 2.1 and 2.5 |
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Solving recurrences and
the Master theorem
Matrix Multiplication |
Monday February 1
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[DPV] Chapter 2.2 and 2.5 |
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Fast Fourier Transform (FFT) |
Wednesday February 3
and Friday February 5 |
[DPV] Chapter 2.6 |
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Median in linear time: |
Monday February 8
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Randomized algorithm is in [DPV] Chapter 2.4 |
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Exam 1: RSA and divide-and-conquer |
Wednesday February 10
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DFS: |
Friday February 12
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[DPV] Chapter 3.1-3.3 |
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DFS: |
Monday February 15
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[DPV] Chapter 3.4 |
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BFS
Dijkstra's algorithm for shortest paths |
Wednesday February 17
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[DPV] Chapters 4.1-4.4 |
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Priority queue (min-heap) implementation
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Friday February 19
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[DPV] Chapter 4.5 |
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Shortest paths with negative length edges:
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Monday February 22
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[DPV] Chapter 4.6 |
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Minimum spanning trees:
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Wednesday February 24
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[DPV] Chapters 5.1.5 and 5.1.2 |
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Minimum spanning trees:
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Friday February 26
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[DPV] Chapter 5.1 |
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Analysis of union-find data structure
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Monday March 1
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[DPV] Chapter 5.1 |
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Exam 2: Graph algorithms |
Wednesday March 3
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Dynamic Programming:
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Friday March 5
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[DPV] Chapters 6.1-6.2 |
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Dynamic Programming:
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Monday March 8
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[DPV] Chapter 6.4 |
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Dynamic Programming:
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Wednesday March 10
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[DPV] Chapters 6.3 and 6.5 |
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Dynamic Programming:
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Friday March 12
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For Floyd-Warshall, see:
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| Review of Dynamic Programming for the exam |
Monday March 15
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Exam 3: Dynamic programming |
Wednesday March 17
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Guest lecture by
Milena Mihail
on
Prof. Mihail will be teaching Advanced Algorithms in the fall, sign up! |
Friday March 19
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[DPV] Chapter 9.2.4 |
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Linear programming:
Duality Simplex algorithm Max flow Max-flow=min-cut Bipartite matching |
Monday March 29
to Friday April 2 |
[DPV] Chapter 7 |
| NP-completeness |
Monday April 5
to Friday April 9 |
[DPV] Chapter 8 |
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NP-completeness of SAT
Undecidability of the halting problem |
Monday April 12
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[DPV] End of Chapter 8.3 |
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Approximation algorithms:
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Wednesday April 14
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See [DPV] Chapter 9.2 for vertex cover approx alg. |
| Bloom filters |
Friday April 16
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See Wikipedia |
| Review for Exam 4 |
Monday April 19
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Exam 4: NP-completeness, linear programming, and max-flow |
Wednesday April 21
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| Markov chains |
Friday April 23
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Quantum computing guest lecture
by Ken Brown |
Monday April 26
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| PageRank |
Wednesday April 28
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| Review for Final Exam |
Friday April 30
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