Computer Science 484

Advanced Algorithms

Spring 2007

Instructor: Daniel Stefankovic (office hours: Tu 2pm-3pm, Th 2pm-3pm).
Time: Tu,Th 12:30pm-1:45pm.
Location: Computer Studies Building 601.

TA and office hours:

Bin Wei (bwei) - Mo 5pm-6pm, We 6pm-7pm.

Textbook: [CLRS01] Introduction to Algorithms (2nd edition), T. Cormen, C. Leiserson, R. Rivest, and C. Stein, 2001.

Other resources/recommended reading:

[KT05] Algorithm Design, J. Kleinberg and E. Tardos, 2005.
[DPV06] Algorithms, S. Dasgupta, C. Papadimitriou, U. Vazirani (a draft is available online), 2006.
[K91] The Design and Analysis of Algorithms, D. Kozen, 1991.
[AHU74] The Design and Analysis of Computer Algorithms, A. Aho, J. Hopcroft, J. Ulman, 1974.
[MU05] Probability and Computing: Randomized Algorithms and Probabilistic Analysis, M. Mitzenmacher, E. Upfal, 2005.
[MR95] Randomized Algorithms, R. Motwani, P. Raghavan, 1995.
[V04] Approximation Algorithms, V. Vazirani, 2004.
[J03] Counting, Sampling and Integrating (Algorithms and Complexity Series), M. Jerrum, 2003.

Prerequisites: CSC484 Design and Analysis of Efficient Algorithms.

Schedule

Date	Topic	Reading Due
Jan. 18 Th	Probability I (basics)	[MR95] Ch. 3, Appendix C; [MU05] Ch. 3; [CLRS01] Appendix C; Babai I
Jan. 23 Th	Probability II (concentration inequalities)	[MU05] Ch. 4	HW 1, due 1/30
Jan. 25 Th	Probability III (balls and bins)	[MU05] Ch. 5
Jan. 30 Tu	Min-Cut, Max-Cut, Fingerprinting	[CLRS01] Ch. 28
Feb. 1 Th	Linear Algebra review	Babai II
Feb. 6 Tu	Markov Chains I (cover time)	[MR95] Sec 6.1-6.5, Lovasz I
Feb. 8 Th	Markov Chains II (mixing time)	[MU05] Ch. 7, Ch. 10
Feb. 13 Tu	Markov Chains III (counting)	[MR95] Ch. 11
Feb. 15 Th	Markov Chains IV (coupling)	[MU05] Ch. 11
Feb. 20 Tu	Markov Chains V (path coupling)
Feb. 22 Th	Markov Chains VI (canonical paths)	[J03] Ch. 5
Feb. 27 Tu	Fourier Transform I (basics)	[CLRS01] Ch. 30
Mar. 1 Th	Fourier Transform II (expanders)	here Sec. 2.1 - 2.4
Mar. 6 Tu	Fourier Transform III
Mar. 8 Th	MIDTERM
(spring break)
Mar. 20 Tu	Algorithms in Number Theory I (basics)	[CLRS01] Ch. 31
Mar. 22 Th	Algorithms in Number Theory II (primality)	[MR95] Ch. 14
Mar. 27 Tu	Algorithms in Number Theory III (FFT)
Mar. 29 Th	Algorithms in Number Theory III (LLL)
Apr. 3 Tu	Linear Programming I (duality, simplex method)	[CLRS01] Ch. 29, [DPV06] Ch. 7
Apr. 5 Th	Linear Programming II
Apr. 10 Tu	Semidefinite Programming	Lovasz II
Apr. 12 Th	Metric Embeddings I	Indyk, Gupta
Apr. 17 Tu	Metric Embeddings II
Apr. 19 Th	Metric Embeddings III
Apr. 24 Tu	Multicommodity flows	[CLRS01] Ch. 26, LLR95
Apr. 26 Th	Computational Algebra (Groebner basis)
May. 1 Tu	String Matching	[CLRS01] Ch. 32
May. 9 We	FINAL EXAM (7:15pm, CSC 601)

Grading

Homework: 30%.
Midterm: 30%.
Final: 40%.

Homework Rules

Homework is collected on the due date, before class.
No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).
In the final evaluation everybody's two lowest homework scores will be dropped.
Each problem must be written on a separate letter-size paper.
You may work with one other person on homeworks, but you must each write up your solutions separately (without any written aid). If you work with another person, indicate who you worked with on your solution (thus you should each indicate each other).

This course follows The University Policy on Academic Honesty .