CS 684 Spring 2009
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.
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 McGraw-Hill Companies, 2nd Edition (2001).
Combinatorial Optimization: Algorithms and Complexity by C. H. Papadimitriou and K. Steiglitz, Englewood Cliffs, Prentice Hall, c1982, Reprinted by Dover Books, 1998
A few recent papers.
| Lectures | Dates | Topics | Lecture Notes | Scopes | Notes |
| 1 | January 21 | Introduction, Graph Concepts | |||
| 2 | January 28 | Graph Traversal Algorithms | Greedy | ||
| 3 | February 4 |
Shortest Path, Minimum Spanning Tree |
Greedy | ||
| 4 | February 11 | All Pairs Shortest Path, Negative Cycles | Dynamic programming | ||
| 5 | February 18 | Network Flows | Iterative | ||
| 6 | February 25 | Bipartite Matching and Nonbipartite Matching | Iterative | ||
| 7 | March 4 | Weighted Matching | Iterative | ||
| March 11 | Spring break | ||||
| 8 | March 18 | Midterm | |||
| 9 | March 25 | Sorting Networks, Zero-One Principles | |||
| 10 | April 1 | NP-Complete Graph Problems, PSPACE | |||
| 11 | April 8 | Special Cases Analysis of Graph Problems | |||
| 12 | April 15 | Approximation Algorithms (TSP, Center Selection Problem, Maximum Cut, etc.) | |||
| 13 | April 22 | Online Algorithms (k-Server Problem, Random Walk) | |||
| 14 | April 29 | Randomized Algorithms (Minimum Cut, Closest Pair, etc.) | |||
| 15 | May 6 |
Final exam (7:30pm - 10:15pm) |
Tentative Grading:
Midterm Exam (30%)
Final Exam (50%)
Assignments (20%)
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