CSC 311 - Algorithms

Shai Simonson    306 Stanger    (508) 565-1008

Email:  shai@stonehill.edu

Homepage: http://web.stonehill.edu/compsci/shai.htm


Lectures:  MWF 9:30 - 10:20, 001 Stanger.

Text:  The Design and Analysis of Algorithms by Anany Levitin, Addison Wesley.  Third Edition

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 be Wednesday, May 10, 9:00 AM, 001 Stanger.

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:  None.


Assignments

assignment 1 assignment 2 assignment_3 assignment 4


Resources

Sorting Video   My Lecture Notes I         My Lecture Notes II     Intro to NP-Complete Notes     Good 2D-Geometry Notes        P Versus NP Page    A List of NP-Complete Problems    My Video Lectures

Brief Syllabus

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.
 

Week

Topic

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, 11.2
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.

Chapters 9.1-9.3
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.

Chapter 8
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, Dominating Set.
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 for KMP.

Chapters 5.4, 6.5