CS 695 Fall 2010
Special Topics on Theoretical Computer Science

Approximation Algorithms

Lecture Time:Tuesdays 7:20pm - 10:00pm
Location: Innovation Hall 134
Course webpage: http://www.cs.gmu.edu/~lifei/teaching/cs695_fall10/
Credit: 3

Instructor: Fei Li, Room 5326, Engineering Building, email: lifei@cs.gmu.edu
Office hours: Thursday 4:15pm - 6:15pm

NEW:

09/28/2010: Due date of assignment 2 has been changed.
09/22/2010: No class on October 12
09/13/2010: Paper list is updated.
09/07/2010: Grading policy is updated.

Course Overview:

The area of approximation algorithms is aimed at giving provable guarantees on the performance of algorithms for hard problems. In this course, we will learn approximation algorithms and their analysis. We will also discuss about online algorithms and competitive analysis.

Prerequisites:

CS 583 or equivalent, or permission of the instructor. Please contact with the instructor if you are not sure.

Recommended Books:

Approximation Algorithms, by Vijay V. Vazirani, Springer, 2003
Introduction to Algorithms, by Thomas H. Corman, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, The MIT Press, 3rd Edition 2009
Probability and Computing: Randomized Algorithms and Probabilistic Analysis, by Michael Mitzenmacher and Eli Upfal, Cambridge University Press, 2005
Randomized Algorithms, by Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press, 1995

Course Materials: (Tentative)

Lectures	Dates	Topics	Scopes	Notes
1	August 31	Introduction of Randomized Algorithms	Preface of MR Chapters 1, 2, 3,1 - 3.3, 5.1 - 5.3 of MU
2	September 7	Approximation Algorithms (Greedy and Local Search) Vertex Cover, Set Cover, Shortest Super-string, Max-Cut	Chapters 1.1, 1.2, 2.1 of V Notes	Assignment 1 released (Problem 35.3 of CLRS)
3	September 14	Approximation Algorithms (Dynamic Programming + Enumeration for PTAS) Knapsack, Bin Packing, Minimizing Makespan	Chapters 8.1, 8.2, 10.1 of V CLRS 35.5 Notes
4	September 21	Approximation Algorithms (Cut-Related Problems) Multiway Cut, k-Cut Approximation Algorithms (LP: Introduction)	Chapters 4.1, 4.2, 12.1 - 12.3 of V Notes	Assignment 1 due Assignment 2 released
5	September 28	Approximation Algorithms (LP-Based: Rounding) Set Cover, Machine Scheduling	Chapters 14.1, 14.2 Sections 4.2, 5 of "Scheduling Algorithms"
6	October 5	Approximation Algorithms (LP-Based: Primal-Dual) Weighted Vertex Cover Approximation Algorithms (SDP-Based) Max-Cut	Notes Chapters 26.1 - 26.4 of V
Columbus Day Recess (Tuesday classes do not meet this week)	October 12
7	October 19	Online Algorithms (Introduction)	Notes CLRS 17 Amortized Analysis 1 Amortized Analysis 2	Assignment 2 due Assignment 3 (CLRS 17-5)
8	October 26	Online Algorithms (Caching, Load Balancing)	Notes
9	November 2	Online Algorithms (Variants of Competitive Analysis) Online Algorithms (Packet Scheduling -- Presentation)	Notes	Assignment 3 due
10	November 9	Steiner Forest (given by Jennifer Campbell)	Presentation Slides
11	November 16	Presentation (5)	Nan Li: A 2.5-Approximation Algorithm for Shortest Super-string Seth Phillips: Competitive Paging Algorithms Brandon Thomson: Algorithms for Power Savings Mike Paton: A Near-Tight Approximation Algorithm for the Robot Localization Problem Venkatrama Kalpathy Balan: Scheduling with Limited Machine Availability
12	November 23	Presentation (4)	Eric Popelka: Randomized Competitive Algorithms for the List Update Problem Len Matsuyama: Energy-Efficient Algorithms Mohammad Haque: System-wide Energy Minimization for Real-time Tasks: Lower Bound and Approximation Eli R. Viertel: Advice Complexity and Barely Random Algorithms
13	November 30	Presentation (5)	Zhi Zhang: On-Line Algorithms in Machine Learning Jennifer Campbell: Optimal Powerdown Strategies James A. Fowler, Jr.: Self-Adjusting Binary Search Trees Eric G. Kangas: A simple Local-Control Approximation Algorithm for Multicommodity Flow Syed Faraz Mahmood: Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems
14	December 7	Project presentations (13)	Nan Li: An Experimental Comparison of Two Approximation Algorithms for the Shortest Superstring Problem Seth Phillips: Experimental Comparison of Metric 2-Server Algorithms Brandon Thomson: Improved Power Management for FreeBSD Mike Paton: Using Evolutionary Computation to Improve the Robot Localization Approximation Algorithm Venkatrama Kalpathy Balan: Stochastic Online Scheduling with Uncertainties Eric Popelka: Load Balancing Len Matsuyama: Empirical Testing of the Energy-Proportional Speed Scaling Algorithms Mohammad Haque: System-wide Energy Optimization for Multiple DVS Components and Real-time Tasks Eli R. Viertel: Resource Contention for Job Shop Scheduling with Unit Length (m-JSS-unit) Zhi Zhang: Scheduling Jobs Under Energy and Flow Time Constraints James A. Fowler, Jr.: Shared Memory Parellel Splay Trees Eric G. Kangas: Implementation and Analysis of the Awerbuch/Leighton Approximation Algorithm for Multicommodity Flow Syed Faraz Mahmood: Genome Assembly with PTAS Euclidean TSP	Final project is due on December 21

Paper List (Papers are to be added in this list along the course):

Approximation Algorithms:

X. Zhang and C. Xu, ``System-wide Energy Minimization for Real-time Tasks: Lower Bound and Approximation'', ACM Transactions on Embedded Computing Systems, Vol 7, No. 3, Article 28, April 2008
D. S. Hochbaum and D. B. Shmoys. ``A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach'', SIAM Journal on Computing, 17(3):539-551, 1988.
Z. Sweedyk, ``A 2.5-Approximation Algorithm for Shortest Super-string'', SIAM Journal on Computing, Vol. 29, No. 3, pp. 954-986, 1999.
S. Koenig, J. S. B. Mitchell, A. Mudgal, and C. Tovey, ``A Near-Tight Approximation Algorithm for the Robot Localization Problem'', SIAM Journal on Computing, Vol. 39, No. 2, pp. 461-490, 2009.
B. Awerbuch, F. T. Leighton, ``A simple Local-Control Approximation Algorithm for Multicommodity Flow'', Proceedings of the 34th IEEE Annual Foundations of Computer Science (FOCS), pages 459-468, 1993.
S. Arora, ``Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems'', Journal of the ACM (JACM), Volume 45, Issue 5, pages 753-783, 1998.
D. S. Hochbaum, ``Approximating Covering and Packing Problems: Set cover, Vertex cover, Independent set, and Related problems'', pages 94-143, in Approximation Algorithms for NP-hard Problems, 1997.
L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein, ``Scheduling to Minimize Average Completion Time: Off-line and Online Approximation Algorithms'', Mathematics of Operations Research, Volume 22, Number. 3, pages 513-544, 1997.
D. Karger, C. Stein, and J. Wein, `` Scheduling Algorithms'', a chapter written for the CRC Handbook on Algorithms, 1997.

Online Algorithms:

A. Fiat, R.M. Karp, M. Luby, L. A. McGeoch, D. Sleator, and N. Young, ``Competitive Paging Algorithms'', Journal of Algorithms, Volume 12, Number 4, pages 685-699, 1991.
N. Reingold, J. Westbrook, D. Sleator, ``Randomized Competitive Algorithms for the List Update Problem'', Algorithmica, Volume 11, Number 1, pages 15-32, 1994.

D. D. Sleator and R. E. Tarjan, ``Self-Adjusting Binary Search Trees'', Journal of the ACM (JACM), Volume 32, Issue 3, pages 652-686, 1985.
Avrim Blum, ``On-Line Algorithms in Machine Learning'', Online Algorithms: The State of the Art, Lecture Notes In Computer Science, Volume 1442, pages 306-325, 1998.
N. Bansal, N. Buchbinder, and J. Naor, ``A Primal-Dual Randomized Algorithm for Weighted Paging'', Proceedings of the 48th IEEE Symposium on Foundations of Computer Science, pages 507-517, 2007.
C. Phillips, C. Stein, E, Torng and J. Wein, ``Optimal Time-Critical Scheduling via Resource Augmentation'', Algorithmica, Volume 32, Number 2, pages 163-200, March 2008.

Green Computing:

S. Albers, ``Energy-Efficient Algorithms'', Communications of the ACM, Vol. 53 No. 5, pages 86-96, 2010.
J. Augustine, S. Irani, and C. Swamy, ``Optimal Powerdown Strategies'', SIAM Journal on Computing, Vol. 37, pages 1499-1516, 2008.
S. Irani, S. K. Shukla, and R. Gupta. ``Algorithms for Power Savings'', ACM Transactions on Algorithms, Vol. 3. 2007.
S. Irani, S. K. Shukla, and R. K. Gupta. ``Online Strategies for Dynamic Power Management in Systems with Multiple Power-Saving States'', ACM Transactions on Embedded Computing Systems. Vol. 2, pages 325-346, 2003.
S. Irani, G. Singh, S. K. Shukla, and R. K. Gupta, ``An Overview of the Competitive and Adversarial Approaches to Designing Dynamic Power Management Strategies'', IEEE Transactions on VLSI Systems, Vol. 13, pages 1349-1361, 2005.
S. Irani and K. Pruhs, ``Algorithmic Problems in Power Management'', SIGACT News Vol. 36, pages 63-76, 2005.
NSF Workshop on the Science of Power Management, 2009
NSF Workshop on the Science of Power Management, 2010
The First International Green Computing Conference, 2010 (See Section 2, Section 5, WIPGC Section 1, WIPGC Section 5, WIPGC Section 7, WIPGC Section 8, only).

Tentative Grading:

Assignments ~~(20%)~~ (30%)
~~Two presentations (40%)~~ One presentation (30%)
A project. You can work on designing and analyzing an approximation algorithm for a NP-hard problem, or designing and analyzing an online algorithm for an online problem, or implementing some known approximation algorithms for some specific applications and provide experimental analysis. (40%)

Academic Honesty:

The integrity of the University community is affected by the individual choices made by each of us. GMU has an Honor Code with clear guidelines regarding academic integrity. Three fundamental and rather simple principles to follow at all times are that: (1) all work submitted be your own; (2) when using the work or ideas of others, including fellow students, give full credit through accurate citations; and (3) if you are uncertain about the ground rules on a particular assignment, ask for clarification. No grade is important enough to justify academic misconduct. Plagiarism means using the exact words, opinions, or factual information from another person without giving the person credit. Writers give credit through accepted documentation styles, such as parenthetical citation, footnotes, or endnotes. Paraphrased material must also be cited, using MLA or APA format. A simple listing of books or articles is not sufficient. Plagiarism is the equivalent of intellectual robbery and cannot be tolerated in the academic setting. If you have any doubts about what constitutes plagiarism, please see me.

Disability Statement:

If you have a learning or physical difference that may affect your academic work, you will need to furnish appropriate documentation to the Disability Resource Center. If you qualify for accommodation, the DRC staff will give you a form detailing appropriate accommodations for your instructor. In addition to providing your professors with the appropriate form, please take the initiative to discuss accommodation with them at the beginning of the semester and as needed during the term. Because of the range of learning differences, faculty members need to learn from you the most effective ways to assist you. If you have contacted the Disability Resource Center and are waiting to hear from a counselor, please tell me.