Lectures: MWF 9:30 - 10:20, ??? College Center.
Text: The Design and Analysis of Algorithms by Anany
Levitin, Addison Wesley. Third
Goals: Algorithms is a natural successor to Data
Structures, and as such, represents the core of what computer
science is all about. Algorithms are fundamental.
Every other area of computer science relates in some way to
algorithms. An algorithm is a step by step solution to a
problem that can be implemented on a computer. Computer
architecture motivates parallel algorithms, networks motivate
distributed algorithms. Algorithms are used in computer
graphics, database theory, AI, compilers, as well as software
engineering of all kinds. Theory of computation helps us
determine which problems have and do not have efficient
algorithms. Sometimes a seemingly small change in the
problem affects whether or not there is an efficient
algorithm. Surprisingly perhaps, some very important
problems have no algorithms at all!
The goal in this class is to understand the fundamental significance of designing and analyzing algorithms in computer science. We study the design of algorithms according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time complexity of an algorithm and the underlying data structures. NP-Completeness theory is examined along with methods of coping with intractability, such as approximation and probabilistic algorithms.
Exams: There will 6 quizzes (25%), the lowest grade
will be dropped, and one final examination (35%). The final will
Assignments: Homework assignments are worth 40% of your grade. You may do homework with a partner (max 2 people per group) , as long as you stick with that same partner the whole semester. When you are asked to write, design or describe an algorithm, you may use a computer language or pseudo-code, or a careful English description. When you are asked to write a program or code, you must actually write the program using whatever tool you like. Read our department's academic integrity guidelines before you hand in any programs.
Grading: You can guarantee an A with 90% a B with 80% etc. I may curve these numbers in your favor, if I feel it is needed.
Special Dates: Friday April 26 - Passover. I will announce alternative plans for this day.
|assignment 1||assignment 2||assignment_3||assignment 4|
Through the prerequisites for this course, you should already know the mathematical material in:
Appendices A and B, Chapter 2, as well as the data structures in Chapter 1, Section 4.
Reading (3rd Edition)
|1-2||Introduction: Polynomial Time Algorithms versus
NP-Complete Problems. Worst Case and Average
Case Time Complexity Analysis. Simple
Algorithms: Max, Min, GCD, Fast-Exponentiation.
Using Recursion. Kadane's algorithm.
||Chapters 1, 2, 3.4
|3-4||Data Structure Review: Stacks, Queues, Priority
Queues, Height Balanced Search Trees, Heaps. Searching
and Sorting: Bubble Sort, Insertion Sort, Selection Sort,
Heapsort, Quicksort, Counting Sort, Bucket Sort, Radix Sort.
||Chapters 1.4, 3.1, 3.2, 4.1,.4.5 5.1, 5.2, 6.4, 7.1, 11.1,
|5-6||Graph Algorithms: Topological Sorting, Depth First
Search and Applications, Breadth First Search.
||Chapters 3.5, 4.2|
|7||Graph Algorithms: Shortest Path, Minimum Spanning
Tree, the Union-Find Data Structure, and Amortized Analysis.
|8||Geometric Algorithms: Line Intersection, Convex
Hull: Jarvis, Graham, Merge Hull.
||Chapters 3.3, 5.5
|9||Quizzes throughout the semester
|10-11||Dynamic Programming: Fibonacci Numbers, Binomial
Coefficients, All Pairs Shortest Path, Knapsack,
Matrix-chain Multiplication, Optimal Triangulation, Fixed
Size Graph Bandwidth. Connection to Queues.
|12||Greedy Methods: Huffman Codes, Minimum Spanning Tree
Revisited, Task Scheduling.
||Chapter 9.4, 12.3
|13-14||NP-Complete Problems and Reductions: 3SAT, Vertex Cover,
3-Colorability, Subset Sum, Hamiltonian Path/Circuit,
Partition, Clique, Independent Set, Not-All-Equal3SAT,
Approximation Algorithms: Vertex cover, Traveling salesman problem (TSP), Applet for TSP Approximation.
|Chapters 3.4, 6.6, 11.3
|15||Other topics if time allows: Mathematical
Algorithms, or String Matching: Knuth Morris Pratt
(KMP), and Boyer-Moore, Applet
||Chapters 5.4, 6.5