CS 483 Fall 2008
Design and Analysis of Algorithms


Lecture Time: Monday and Wednesday 1:30pm - 2:45pm
Location: Innovation Hall 136
Course webpage: http://www.cs.gmu.edu/~lifei/teaching/cs483_fall08/
Credit: 3

Instructor: Fei Li, Office 443 ST II, email: lifei@cs.gmu.edu
Office hours: Friday 4:00pm - 6:00pm

Teaching Assistant: TBD
Office hours: TBD

NEW:
07/31: Note new textbooks.
Course overview:

In this course, a thorough examination of several well-known techniques that are used for the design and analysis of efficient algorithms will be covered. Topics to be covered include theoretical measures of algorithm complexity, sorting and selection algorithms, greedy algorithms, divide and conquer techniques, dynamic programming, linear programming, graph algorithms, search strategies, and an introduction to the theory of NP-completeness, algorithms for algebraic problems, probabilistic methods, and approximation algorithms.

Prerequisites:

CS 310 and CS 330 Calculus (MATH 113, 114, 213) and MATH 125. Please contact with the instructor if you are not sure.

Required Textbook:

Algorithms by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani, The McGraw-Hill Companies (2008). A draft of the book can be found at http://www.cs.berkeley.edu/~vazirani/algorithms.html

Highly Recommended Textbook:

Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, The McGraw-Hill Companies, 2nd Edition (2001).
Course Materials:
 
Lecture Date Topic Lecture Notes Scope Assignments Note
1 Aug. 25 Introduction   DPV 0    
2 Aug. 27 Algorithms with numbers   DPV 1.1 - 1.3 Assignment 1  
3 Sep. 1 Algorithms with numbers   DPV 1.4 - 1.5    
4 Sep. 3 Randomized analysis   CLSR 5 Assignment 2. Assignment 1 due.
5 Sep. 8 Randomized analysis   CLSR 5    
6 Sep. 10 Divide and conquer   DPV 2.1 - 2.4 Assignment 3. Assignment 2 due.
7 Sep. 15 Divide and conquer   DPV 2.5 - 2.6    
8 Sep. 17 Fourier tranform   CLSR 30    
9 Sep. 22 DFS and SCC   DPV 3 Assignment 4. Assignment 3 due.
10 Sep. 24 BFS and Dijkstra   DPV 4.1 - 4.5    
11 Sep. 29 Shortest paths   DPV 4.6 - 4.7 Assignment 5. Assignment 4 due.
12 Oct. 1 Greedy   DPV 5    
13 Oct. 6 Matroid   CLSR 16    
14 Oct. 8 Amortized analysis   CLSR 17   Assignment 5 due.
  Oct. 13 Midterm      

Monday class meets Tuesday. DPV 1 - 5, CLSR 5, 16, 17, 30
15 Oct. 15 Dynamic programming   DPV 6.1 - 6.4    
16 Oct. 20 Dynamic programming   DPV 6.5 - 6.7 Assignment 6.  
17 Oct. 22 Linear programming   DPV 7.1 - 7.3    
18 Oct. 27 Linear programming   DPV 7.4 - 7.7 Assignment 7. Assignment 6 due.
19 Oct. 29 Linear programming   CLSR 29    
20 Nov. 3 NP-completeness   DPV 8.1 - 8.2 Assignment 8. Assignment 7 due.
21 Nov. 5 NP-completeness reduction   DPV 8.3    
22 Nov. 10 NP-completeness reduction   CLSR 34    
23 Nov. 12 Approximation algorithms   DPV 9.1 - 9.2 Assignment 9. Assigment 8 due.
24 Nov. 17 Approximation algorithms   DPV 9.3    
25 Nov. 19 Approximation algorithms   CLSR 35    
26 Nov. 24 Approximation algorithms   CLSR 35   Assignment 9 due.
  Nov. 26         No class. Thanksgiving.
27 Dec. 1 Quantum algorithms   DPV 10    
28 Dec. 3 Review        
  Dec. 8         No class. Reading days.
  Dec. 10 Final exam      

Wednesday 1:30pm - 4:15pm. DPV 1 - 9, CLSR 5, 16, 17, 29, 34, 35

Topics:

In this course, we will consider the algorithm design and alaysis techniques of various problems coming from the following areas:
• Analysis of Algorithm Efficiency (asymptotic notation, amortized analysis)
• Brute Force Techniques (sorting, search, traveling salesmen)
• Divide and Conquer (merge sort, quicksort, matrix multiplication, polynomial multiplication)
• Numerical algorithms (modulo arithmetic, RSA)
• Graph decomposition and search (connected components, shortest path problem)
• Greedy Techniques (minimum spanning tree, Huffman trees)
• Dynamic Programming (edit distance,matrix chainmultiplication, knapsack, all pairs shortest paths)
• Linear Programming (network flows, matching, simplex, duality)
• Randomized Algorithms
• Limitations of Algorithm Power (lower bounds, P, NP)
• Coping with Limitations (approximation algorithms)

Course Outcomes:

1. An understanding of classical problems in Computer Science
2. An understanding of classical algorithm design and analysis strategies
3. An ability to analyze the computability of a problem
4. Be able to design and analyze new algorithms to solve a computational problem
5. An ability to reason algorithmically

Tentative Grading:

Weekly assignments (45%)

Midterm Exam (20%)

Final Exam (35%)
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.