MCS-375: Algorithms (Fall 2009)

In this course we will learn how to design and analyze efficient algorithms, and prove their correctness. We achieve this by studying some combinatorial algorithms and the general design techniques they illustrate. We will study algorithms that are

symbolic & discrete, as opposed to numeric & continuous, and
sequential, as opposed to parallel.

We will ask and answer questions such as the following.

How might a good algorithm for a new problem be found?
How do we analyze the resouce usage of an algorithm?
How do we prove that an algorithm actually does what it's supposed to do?
How do we compare the resource usage of different algorithms that solve the same computational problem?
Which of the many different ways of solving the same problem is better?

We will learn these skills almost exclusively by working concrete example problems, introducing the tools as we discover uses for them. Although this course is of great practical utility, we will focus on honing our abilities of mathematical analysis and design of data structures and algorithms outside of the context of a specific computer platform or programming language.

Prerequisite

MCS-178: Introduction to Computer Science II

Text

The official textbook is Introduction to Algorithms, 2nd edition, by T.H. Cormen, C.E. Leiserson, R.L. Rivest & C. Stein; McGraw-Hill, NY, 2001. I'll also be distributing my own notes to supplement the text.

References

The following books are suggested supplementary readings. They are available from the library or from me.

Algorithm Design, by Jon Kleinberg and Éva Tardos; Pearson/Addison-Wesley, 2006
Algorithms, by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani; McGraw-Hill, 2007

Reaching me

The class web page is at http://homepages.gustavus.edu/~sskulrat/2009F-375/index.html. All office, phone and schedule information will be maintained there. I'll keep it updated with any temporary changes to my schedule. If my office door is open you are welcome. If I'm busy, we'll set up an appointment. Email and phone calls work too.

Honor

I expect you to adhere to the highest standards of academic honesty and to uphold the Gustavus Honor Code. In doing an assignment, you may discuss problems and their solutions with fellow students or even your professors, but you should make an effort to solve each problem on your own. Give credit to any people and/or any other reading sources that help you find solutions, be they textbooks, journals, or internet postings. Be explicit and acknowlege clearly what sort of help you received. Failure to do so will be considered cheating.

A first violation of the honor code will result in a grade of 0 on the paper, homework, or exam in question. Any further violations will result in an automatic F for the course and a notification to the Dean's Office.

Assignments and Grading

There will be regular homework assignments (30%), two intra-term exams (40%), and one final (30%). All exams are closed book and in-class. If you get 80% or more of the points, you will earn an A, 75% for an A-, 70% for a B+ and down by 5 percentage points each to the lowest passing grade of 35% for a D. There is no curve. However, I reserve the right to subjectively adjust your final grade.

Homework will be of the modified mastery type. You have two chances at each homework problem. Each homework set has a due date. You have to hand in your answer by the due date in order to receive any point. If you have not solved the problems in that set completely, hand in your best attempt at a solution. I will return your submission with a remark whether it is satisfactory. If a problem needs more work, and you aren't sure what sort of work it still needs, you should treat that as an invitation to come talk. Once you've done the additional work, you may turn in your new answer within one week after I handed back your ititial submission. Your work will be graded only when you resubmit it the second time.

I encourage you to work with other students on the homework provided that you do so in such a way that every one in your group learns the material. The most effective way to do this is to first discuss each problem as a group and then have each person work on the problem individually. When you're done (or stuck) compare your work and discuss it. Remember that doing the homework is how you learn the material; and that you are not allowed to work cooperatively on tests.

If you do work with other students on the homework, I would like you to follow these guidelines:

Each person should write up the answers independently.
Each person should be able to work each one of the problems independently.
Each person gives credit to the others who helped.

Topics

A tentative outline of topics is as follows:

Computation Machine Model & Asymptotics: RAM machine model, worst case asymptotic analysis, complexity classes
Graph & network algorithms: depth-first search, breadth-first search, strongly connected components, shortest paths, minimum spanning trees
Greedy algorithms: activity scheduling, Huffman's algorithm
Dynamic programming: recurrences, computerized typesetting, text processing, matrix chain multiplication & optimum binary search trees
Data structures: splay trees, red-black trees, augmented search trees, binary heaps, B-trees
Searching & Sorting
Number theory and cryptography: Euclid's algorithm, modular exponentiation, RSA cryptosystem, primality testing
Approximation algorithms: vertex covers, travelling salesman problem

Disability Accommodations

Section 504 of the Rehabilitation Art of 1973 and the Americans with Disabilities Act (1990) work together to ensure reasonable accommodation and non-discrimination for students with disabilities in higher education. A student who has a physical, psychiatric/emotional, medical, learning, or attentional disability that may have an effect on the student's ability to complete assigned course work should contact Laurie Bickett (lbickett@gustavus.edu or x6286), the Disability Services Coordinator in the Advising Center, who will review the concerns and decide with the student what accommodations are necessary.

ELL Accommodations

Help for Students Whose First Language is not English. The Writing Center has on staff a part-time tutor with professional training in ESL/ELL instruction. Students can schedule work with this tutor by contacting the Writing Center. Students may bring their instructors documentation concerning their ELL status. Where it is appropriate, I will allow such students more time to complete either in- or out-of-class writing assignments. For further information, contact the Academic Advising Office.