CS 684 Spring 2010
Graph Algorithms
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.
Some handouts.
Algorithm Design by Jon Kleinberg and Eva Tardos, Pearson Education, Inc. (2006). (You can find the sample chapters on the webpage.)
Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, The McGrawHill 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
Week  Date  Content  Reading materials  Assignments 
no class Martin Luther King Day 
01/18  
1  01/25 (introduction)  KT 1, 2  
2  02/01 (background) 
Mathematical Background 
CLRS 19 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 BellmanFord Shortest Paths 
CLRS 23 and handout CLRS 24 

6  03/01 
AllPairs Shortest Paths and the FloydWarshall 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 
MinCost Flow MinCost Flow Applications 
handout 

10  04/05 (reduction) 
Languages and the Class NP NPCompleteness 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 kCenter Problem 
CLRS 35 and KT 11  
14  05/03 
SubsetSum 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.
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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.