CS 684 Spring 2010

Graph Algorithms


Lecture Time: Monday 7:20pm - 10:00pm
Location: Innovation Hall 206
Course webpage: http://www.cs.gmu.edu/~lifei/teaching/cs684_spring10/
Credit: 3

Instructor: Fei Li, Room 5326, Engineering Building, email: lifei@cs.gmu.edu
Office hours: Monday 5:00pm - 7:00pm


NEW:

 


Course Overview:

This is an advanced course in the design and analysis of efficient algorithms. The emphasis is on algorithms for standard graph problems, such as minimum spanning trees, shortest paths, network flow, and maximum matching. We will also study advanced data structures, which are crucial for the more advanced topics. Randomized algorithms will also be discussed.

Prerequisites:

CS 583. Please contact with the instructor if you are not sure.

Textbook:

Some handouts.

Algorithm Design by Jon Kleinberg and Eva Tardos, Pearson Education, Inc. (2006). (You can find the sample chapters on the webpage.)

Highly Recommended Reference Books:

Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, The McGraw-Hill Companies, 3rd Edition (2009).

Combinatorial Optimization: Algorithms and Complexity by C. H. Papadimitriou and K. Steiglitz, Englewood Cliffs, Prentice Hall, c1982, Reprinted by Dover Books, 1998

Course Materials (Tentative):
Week Date Content Reading materials Assignments

no class

Martin Luther King Day

01/18      
1 01/25 (introduction)

Introduction to Algorithm Design

Stable Marriage Problem

Basics of Algorithm Design

KT 1, 2  
2 02/01 (background)

Mathematical Background

CLRS 1-9

handout

 
3 02/08 (greedy)

Basic Graph Algorithms: BFS and DFS

Applications of DFS

KT 3

CLRS 22

 
4 02/15

Minimum Spanning Trees and Kruskal's Algorithm

Dijkstra's Algorithm for Shortest Paths

KT 4.4 - 4.6 and CLRS 23, 24

 
5 02/22 (dynamic programming)

Prim's and Baruvka's Algorithms for MSTs

Bellman-Ford Shortest Paths

CLRS 23 and handout

CLRS 24

 
6 03/01

All-Pairs Shortest Paths and the Floyd-Warshall Algorithm

Minimum Weight Triangulation

CLRS 25

handout

 

no class

Spring break

03/08      
7 03/15

Midterm

   
8 03/22 (network flows)

Network Flows

Applications and Extensions of Network Flow

CLRS 26 and KT 7

 
9 03/29

Min-Cost Flow

Min-Cost Flow Applications

handout

 
10 04/05 (reduction)

Languages and the Class NP

NP-Completeness Reductions

CLRS 34 and KT 8

 
11 04/12

Cook's Theorem, 3SAT, and Independent Set

Clique, Vertex Cover, and Dominating Set

CLRS 34 and KT 8

 
12 04/19 (approximation)

Hamiltonian Path

Vertex Cover and TSP

CLRS 35 and KT 11

 
13 04/26

Set Cover and Bin Packing

The k-Center Problem

CLRS 35 and KT 11  
14 05/03

Subset-Sum Approximation

Review

CLRS 35

 
15

05/10

7:30 pm – 10:15 pm

Final exam or project (TBD)    
 

Tentative Grading:

Midterm Exam (30%)

A final exam (30%)

Class presentation or assignments (30%)

Class attendence (10%)

No makeup exams will be given for missed tests.

Policies:
 
Hand in hard copies of assignments in class. Please note that all coursework is to be done independently. Plagiarizing the homework will be penalized by maximum negative credit and cheating on the exam will earn you an F in the course. See the GMU Honor Code System and Policies at http://www.gmu.edu/catalog/acadpol.html and http://www.cs.gmu.edu/honor-code.html. You are encouraged to discuss the material BEFORE you do the assignment. As a part of the interaction you can discuss a meaning of the question or possible ways of approaching the solution. The homework should be written strictly by yourself. In case your solution is based on the important idea of someone else please acknowledge that in your solution, to avoid any accusations.
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.