CS 583 Fall 2009
Analysis of Algorithms (Graduate Course)
11/24/09: Lecture notes for Chapters 22 - 25 are uploaded.
11/18/09: Assignment 4 is updated.
11/17/09: Assignment 4 is released.
11/10/09: Lecture note for Chapter 16 is uploaded.
11/03/09: Lecture note for Chapter 15 is uploaded.
11/02/09: Assignment 3 is updated.
10/29/09: Assignment 3 is released.
10/27/09: Lecture notes for Chapters 16 and 23 are uploaded.
10/06/09: Topics on Chapters 12 and 13 will be discussed after the midterm exam.
10/04/09: Lecture notes for Chapters 12 and 13 are uploaded.
09/27/09: Lecture notes for Chapters 8 and 9 are uploaded.
09/23/09: Assignment 2 is released.
09/22/09: Lecture notes for Chapters 6 and 7 are uploaded.
09/22/09: Lecture note for Chapter 11 is updated.
09/15/09: Lecture notes for Chapters 5 and 11 are uploaded.
09/11/09: Problems in assignments are from CLRS 2nd Edition.
09/08/09: Assignment 1 is released.
09/08/09: Lecture note for Chapter 4 is uploaded.
09/02/09: Lecture notes for the Appendix and Chapter 3 are uploaded.
08/30/09: Lecture notes will be posted on this website after each class.
In this course, a thorough examination of several well-known techniques that are used for the design and analysis of 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, graph algorithms, search strategies, and an introduction to the theory of NP-completeness. Additional topics may be covered if time permits. Students are expected to have taken prior undergraduate courses in data structures, as well as calculus and discrete mathematics.
Prerequisites:
CS 310 and CS 330 Calculus (MATH 113, 114, 213) and MATH 125. Please contact with the instructor if you are not sure.
Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, The McGraw-Hill Companies, 2nd Edition (2001), or 3rd Edition (2009)
Algorithm Design by Jon Kleinberg and Eva Tardos, Pearson Education, Inc. (2006). (You can find the sample chapters on the webpage.)
Combinatorial Optimization: Algorithms and Complexity by C. H. Papadimitriou and K. Steiglitz, Englewood Cliffs, Prentice Hall, c1982, Reprinted by Dover Books, 1998
| Lectures | Dates | Topics | Lecture Notes | Scopes | Notes |
| 1 | September 1 | Background
Insertion Sort Merge Sort Asymptotic Notation |
Appendix
CLRS 2 CLRS 3 |
CLRS 1-3 | |
| 2 | September 8 | Divide and Conquer | CLRS 4.1 - 4.3 | Assignment
1:
Problem 2-2; Exercise 3.2-7; Problem 3-3; Exercise 4.1-5; Problem 4-1 (c), (d), (e), (f); Problem 4-4 (a), (c); and one more problem CLRS 4 |
|
| 3 | September 15 | Probabilistic
Analysis
Randomized Algorithm Hashing |
CLRS
5.1 - 5.3
CLRS 11.3 |
CLRS 5 | |
| 4 | September 22 |
Heap Sort Quick Sort |
CLRS 6.1 - 6.4 CLRS 7.1 - 7.3 |
Chapter 11 (slides only) CLRS 6, 7 |
|
| 5 | September 29 | Sorting
in Linear Time
Medians Order Statistics |
Linear-Time Sorting |
CLRS 8.1 - 8.3 CLRS 9 |
CLRS 8, 9 |
| 6 | October 6 | Review |
|
Assignment 2 due CLRS 12, 13, 14 |
|
| October 13 |
|
|
Cancelled due to Columbus Day |
||
| 7 | October 20 |
Midterm exam (7:30pm - 10:00pm) CLRS 15 |
|||
| 8 | October 27 | Greedy Algorithms |
CLRS 16.1 - 16.3 |
CLRS 16 |
|
| 9 | November 3 |
Dynamic Programming |
CLRS 15 |
Assignment
3:
Exercises 16.1-2, 16.1-3, 16.1-4, 16.3-3, and CLRS 17 |
|
| 10 | November 10 | Binary
Search Tree
Red-Black Tree |
CLRS 12.1 - 12.3 CLRS 13 |
CLRS 19, 21 |
|
| 11 | November 17 |
Amortized Analysis Fibonacci Heaps Minimum Spanning Tree |
CLRS 17 CLRS 23 |
Assignment 3 due Assignment 4: Problems 15-2, 15-3, 15-4, and one problem on amortized analysis CLRS 22, 23 |
|
| 12 | November 24 |
Graph Algorithms Shortest Paths |
CLRS 22 CLRS 24 |
CLRS 24, 25 |
|
| 13 | December 1 |
All Pairs Shortest Paths Maximum Flow |
CLRS 25.1, 25.2 CLRS 26.1 - 26.3 |
Assignment 4 due CLRS 26 |
|
| 14 | December 8 |
Review |
Review | ||
| 15 | December 15 |
Final exam (7:30pm - 10:00pm) |
Tentative Grading:
Midterm Exam (30%)
Final Exam (30%)
Assignments (40%)
No make-up exams for missed tests.
No late assignments graded.
Topics Covered:
|
Function
growth: O, theta, omega notation
|
CLRS 3
|
|
Recurrence
relations
|
CLRS 4
|
|
Probabilistic
analysis; randomized algorithms
|
CLRS 5
|
|
Amortized
analysis
|
CLRS 17
|
|
Dynamic
programming
|
CLRS 15
|
|
Greedy algorithms
|
CLRS 16.1-3
|
|
Sorting
heapsort, quicksort, mergesort
|
CLRS 2,
6, 7
|
|
Non-comparison-based
|
CLRS 8
|
|
Selection/order
statistics
|
CLRS 9
|
|
Data structures
balanced binary search trees
|
CLRS 12,
13
|
|
Hash tables
|
CLRS 11
|
|
Heaps /
priority queues
|
CLRS 6.5,
20
|
|
Graph algorithms:
BFS/DFS
|
CLRS 22
|
|
Minimum
spanning tree
|
CLRS 23
|
|
Shortest
paths
|
CLRS 24,
25
|
|
Maximum
flow
|
CLRS 26.1-3
|
|
Time Complexity,
NP-Complete
|
CLRS 34
|
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