Computer Science 284/484

Advanced Algorithms

Spring 2016

Instructor: Daniel Stefankovic
Class: Tuesday, Thursday 12:30pm-13:45pm, Wilmot 116.
Instructor office hours (CSB 620): Tuesday, Thursday 2pm-3pm, CSB 620, or by appointment.
TAs: Zahra Razavi (srazavi@cs.rochester.edu) and Hassler Thurston (jthurst3@u.rochester.edu)
TA office hours (CSB 631): Monday 5pm-6pm, Wednesday 5pm-6pm, or by appointment.


Textbooks: there is no required textbook; see each section for the recommended reading (mostly online; I will also supply handouts).

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.
• [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.


• [MU05] Probability and Computing: Randomized Algorithms and Probabilistic Analysis, M. Mitzenmacher, E. Upfal, 2005.
• [MR95] Randomized Algorithms, R. Motwani, P. Raghavan, 1995.
• [H02] Finite Markov chains and algorithmic applications, O. Häggström, 2002.
• [G97] Counting, sampling and integrating: algorithms and complexity, M. Jerrum, 2003.


• [WS11] The Design of Approximation Algorithms, D.Williamson, D. Shmoys, 2011
• [V04] Approximation Algorithms, V. Vazirani, 2004.


• [BE98] Online Computation and Competitive Analysis, A. Borodin, R. El-Yaniv, 1998.
• [M05] Data Streams: Algorithms and Applications, S. Muthukrishnan, 2005.


• [BCKO08] Computational Geometry: Algorithms and Applications, M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, 2008.
• [G97] Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology, D. Gusfield, 1997.

Prerequisites: CSC282.

Schedule

TOPIC 1: Randomized algorithms introduction

reading: Finite Probability Spaces (Babai).
homework: Homework 1.
homework: Homework 2.


Jan. 14 Th - Basics of probability theory I.

Jan. 19 Tu - Basics of probability theory II.
Jan. 21 Th - Monte Carlo


TOPIC 2: Streaming algorithms

reading: Streaming Algorithms (Chakrabarti), chapters 1-5.


Jan. 26 Tu - Distinct elements.
Jan. 28 Th - Sketching.

Feb. 2 Tu - Frequency moments.


TOPIC 3: Markov Chains

reading: MCMC course (Vigoda); lectures 6,7,8,9,11.


Feb. 4 Th - Random walks, cover time, hitting time.

Feb. 9 Tu - Markov chains I (basics: stationary distribution, detailed balance condition, ergodicity)
Feb. 11 Th - Markov chains II (mixing time)

Feb. 16 Tu - Markov chains III (bounds on mixing time)
Feb. 18 Th - Markov chains IV (coupling from the past)

Feb. 23 Tu - MIDTERM I (covering topics 1,2,3)

TOPIC 4: Geometric algorithms

reading:


Feb. 25 Th - Sweep method; line-segment intersections.

Mar. 1 Tu - Convex hulls I.
Mar. 3 Th - Convex hulls II.
Mar. 8 Tu - SPRING BREAK
Mar. 10 Th - SPRING BREAK



TOPIC 5: String Algorithms

reading:


Mar. 15 Tu - String algorithms - introduction.
Mar. 17 Th - Suffix trees I.

Mar. 22 Tu - Suffix trees II.
Mar. 24 Th - Suffix arrays.



TOPIC 6: Optimization

reading: chapter 29 in [CLRS09], chapters 21 and 26 in [V04].


Mar. 29 Tu - Linear Programming.
Mar. 31 Th - Semidefinite programming (Max Cut).

Apr. 5 Tu - Metric Embeddings.
Apr. 7 Th - Sparsest Cut.

Apr. 12 Tu - MIDTERM II (covering topics 4,5,6)

TOPIC 7: Fun (not covered on exams)

Apr. 14 Th - TBD
Apr. 19 Tu - TBD

Apr. 21 Th - TBD
Apr. 26 Tu - TBD

Grading

The grade for the course is the combination of the exam grade (two midterms; no final) and the homework grade (theoretical and applied).

Homework Rules

• Theoretical homework is collected on the due date, before class.
• Applied (implementation) homework should be emailed to both TA and the instructor by the deadline (specific for each assignment).
• No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).
• You may work with other people on the theoretical 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.
• You must work alone on the applied (implementation) homework. Do not discuss the problem with anybody (except me), do not search for a solution online, do not use any written material when writing any part of the code (for example, no copy-paste, no open textbook when writing code, no reediting of an old source file from an old project, etc).

Test Rules

• All tests are closed book. No text or notes, no scratch paper allowed.

This course follows The University Policy on Academic Honesty .