Computer Science 284/484
Advanced Algorithms
Spring 2013
Instructor:
Daniel Stefankovic Class: Tuesday,
Thursday 12:30pm13:45pm, CSB 632.
Instructor office hours (CSB 620): 10am11am Monday, Wednesday, or by appointment.
TA:
Rahman Lavaee
TA office hours (CSB 726): 23pm Monday, Wednesday, or by appointment.
Textbooks: there is no required textbook; see each section for the recommended reading.
Other resources/recommended reading (most on a 2 hour reserve in the library):

[CLRS09]
Introduction to Algorithms (3rd edition),
T. Cormen, C. Leiserson, R. Rivest, and C. Stein, 2009.

[MU05]
Probability and Computing: Randomized Algorithms and
Probabilistic Analysis, M. Mitzenmacher, E. Upfal, 2005.

[MR95]
Randomized Algorithms, R. Motwani, P. Raghavan,
1995.

[WS11]
The Design of Approximation Algorithms, D.Williamson, D. Shmoys, 2011

[V04]
Approximation Algorithms, V. Vazirani, 2004.

[K91]
The Design and Analysis of Algorithms, D. Kozen,
1991.

[KT05]
Algorithm Design, J. Kleinberg and E. Tardos, 2005.
 [AHU74] The Design and Analysis of Computer
Algorithms, A. Aho, J. Hopcroft, J. Ulman, 1974.
 [BE98] Online Computation and Competitive Analysis, A. Borodin, R. ElYaniv, 1998.
 [M05] Data Streams: Algorithms and Applications, S. Muthukrishnan, 2005.
Prerequisites: CSC282.
Schedule
TOPIC: Randomized algorithms
reading: chapters 1,2,3,5, and appendix in [CLRS09], chapters 1,2,3,4,7 in [MU05], chapters 1,3,4,6.1,6.2,6.3,6.4,6.5,7.2,7.3 in [MR95].
Jan. 17 Th  172/282 diagnostic exam (basic data structures, graph algorithms, and dynamic programming), only required for students taking the class on the 400 level.
Jan. 22 Tu  Basics of probability theory, randomized mincut algorithm.
Jan. 24 Th  Expectation, coupon collector, randomized quicksort, randomized median.
Jan. 29 Tu  Polynomial identity testing (testing matrix product, matchings using Tutte matrix, Isolation Lemma).
Jan. 31 Th  Concentration inequalities, Monte Carlo.
Feb. 5 Tu  Random walks, cover time, hitting time.
Feb. 7 Th  Markov chains, mixing time.
TOPIC: Optimization
reading: chapter 29 in [CLRS09], chapters 21 and 26 in [V04].
Feb. 12 Tu  Linear Programming.
Feb. 14 Th  Semidefinite programming (Max Cut).
Feb. 19 Tu  Metric Embeddings.
Feb. 21 Th  Sparsest cut.
Feb. 26 Tu  EXAM #1 (topics from Jan. 22  Feb. 21)
TOPIC: Data Structures
Feb. 28 Th  Union Find.
Mar. 5 Tu  Dynamic connectivity in amortized O(log^2 n) time.
Mar. 7 Th  Bloom Filters.
Mar. 12 Tu  SPRING BREAK.
Mar. 14 Th  SPRING BREAK.
Mar. 19 Tu  Skip lists.
TOPIC: Online Algorithms
reading: Chapters 1,2,3,4,10 in [BE98], chapter 13 in [MR95].
Mar. 21 Th  Ski rental.
Mar. 26 Tu  Caching, paging, kserver.
TOPIC: Streaming algorithms
reading: Chapters 1,2,3,4 in [M05].
Mar. 28 Th  Heavy hitters.
Apr. 2 Tu  Frequency moments.
Apr. 4 Th  EXAM #2 (topics from Feb. 28  Apr. 2)
TOPIC: Sampling algorithms
reading: chapters 10,11 in [MU05], chapter 11 in [MR95]
Apr. 9 Tu  Determinant based algorithms, spanning trees, matchings in planar graphs.
Apr. 11 Th  Markov Chains, mixing time.
Apr. 16 Tu  Coupling I.
Apr. 18 Th  Coupling II.
Apr. 23 Tu  Path coupling.
Apr. 25 Th  Coupling from the past I.
Apr. 30 Tu  Coupling from the past II.
May. 8 Wed  comprehensive FINAL EXAM, 7:15pm, CSB 632.
Grading
The
grade for the course is the combination of the
exam grade and the
homework grade.
Each exam (midterm) contributes 25% to the exam grade; the final exam contributes 50% to the exam grade.
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
the lowest homework score will be
dropped.
 You may work with other people on the
homework, but you must each write up your solutions separately
(without any written aid). If you work with other people, indicate
who you worked with on your solution.
Test Rules
 All tests are closed book. No text
or notes, no scratch paper allowed.
This course follows
The University Policy on Academic Honesty .