office: 75
email: offner "at" cs.umb.edu
home phone: (978) 443-4697

All the on line material for this course will be found on the web at http://www.cs.umb.edu/~offner/cs624.

• Week 1:
  • Reading:
    • Monday: Chapters 1-2 of the text (Cormen et al.); Chapter 1 through section 1.3 of Skiena.
    • Wednesday: Chapters 3-4 of the text; the rest of Chapter 1 of Skiena.
  • Assignment due February 4: Introduction, some preliminary examples of analysis of algorithms, order of growth of functions, recursions and growth of their solutions, generating functions.

• Week 2:
  • Reading: Chapter 6 of the text (Heapsort).
  • Assignment due February 11: Heaps, Heapsort, and Priority Queues.

• Week 3:
  • Reading (in addition to what is handed out in class):
    • Chapter 7 of the text (Quicksort).
    • At least the first 5 pages of my expository paper "Some Early Analytic Number Theory", which you can find on my web page.
  • Assignment due February 20: Quicksort (mainly).

• Week 4:
  • Reading (in addition to what is handed out in class):
    • Chapter 8, Sections 1 and 4 of the text.
    • Pages 34-39 of Skiena.
  • Assignment due February 25: a little more on sorting.

• Week 5:
  • Reading (in addition to what is handed out in class):
    • Chapter 11 (hash tables), up through page 231. We won't cover the rest.
    • Chapter 12 (binary search trees), up through section 12.3 (page 264).
  • Assignment due March 3: Hash trees and binary search trees.

• Week 6:
  • Reading (in addition to what is handed out in class):
    • Chapter 12 (binary search trees), section 12.4. Actually, you don't have to read this, since it's covered completely in the notes from the class, and I think the notes are more understandable. But that's the material in any case.
    • Chapter 15 (dynamic programming): the introduction (pages 323-324), and sections 15.3 and 15.4.
    • Skiena, sections 3.3, 3.4, and 3.5. These are three war stories involving dynamic programming. You don't have to follow all the details, but you should at least look these over to get a flavor for how this works (and how a master practitioner approaches problems).
  • Assignment due March 10: Binary search trees and dynamic programming.

• Week 7:
  • Monday, March 10: Review day. Bring questions to class!
  • Wednesday, March 12: Mid-term exam. This will be a "closed-book" exam. Bring nothing with you except something to write with.

• Week 8:
  • Reading (in addition to what is handed out in class):
    • Chapter 16 (greedy algorithms), sections 16.2 and 16.3. 16.3 is what is covered in the class handout.
    • Chapter 17 (amortized analysis): We're covering most of this in class on Wednesday. You can skip the parts we don't cover in class.
  • Assignment due April 2: Greedy algorithms and dynamic programming.

• Week 9:
  • Reading (in addition to what is handed out in class):
    • Chapter 22 (elementary graph algorithms; breadth-first search), sections 22.1 and 22,2.
  • Assignment due April 7: Move-To-Front, the Sleator-Tarjan theorem, and breadth-first search.

• Week 10:
  • Reading (in addition to what is handed out in class):
    • Chapter 22 (elementary graph algorithms; depth-first search and some applications), sections 22.3 and 22.4.
  • Assignment due April 14: Depth-first search.

• Week 11:
  • Reading (in addition to what is handed out in class):
    • Chapter 22, section 22.5 (The Kosaraju algorithm for strongly connected components).
    • Chapter 23. Minimum spanning trees. We will cover only Prim's algorithm, so you can skip Kruskal's algorithm.
  • Assignment due April 23: strongly connected components and minimum spanning trees.

• Week 12:
  • Reading (in addition to what is handed out in class):
    • Chapter 15, section 15.5
    • If you still haven't read Skiena, sections 3.3, 3.4, and 3.5, do it now!
  • Assignment due April 28: Optimal binary search trees, another problem involving dynamic programming, and yet another simple graph problem.

• Week 13: NP-completeness
  • Reading (in addition to what is handed out in class):
    • Chapter 34. However, I will be doing things slightly differently from how the book does it. So you should look over the chapter, but don't feel you have to know it cold. In particular, I would skip the section on "circuit satisfiability", and also the discussion of languages. And don't bother about anything we haven't gotten to in class. We will come to it all later.
    • Skiena has an excellent discussion of NP-complete problems in Chapter 6. And actually what I will be doing in class is closer to his treatment than to CLRS.
  • Assignment due May 12: NP-completeness.

• Week 14: More on NP-completeness
  • Reading (in addition to what is handed out in class):
    • You really don't have to read anything other than what I suggested last week. Absolutely do read Skiena if you haven't yet. He's always interesting to read, and you can learn a lot from him.
  • There is no assignment this week. Study for the final!

• CS L320: Applied Discrete Mathematics

This prerequisite is important. If you have not had it, and done well in it, you should not be enrolled in this course.

Class meetings: M/W 7:00-8:15 PM in room M-1-420

Office hours: Before class: M/W 6:00-6:45 PM

The first text is required:
Introduction to Algorithms, Second Edition
by Cormen, Leiserson, Rivest, and Stein
McGraw-Hill, 2001

The second text is not required, but is highly recommended. It has a lot of good "war stories" in it, and gives a good feeling for the subject:
Algorithm Design Manual (with CD)
by Steve S. Skiena
Springer-Verlag, 1998

At a minimum, I plan to cover the following material this term:

1. Introductory material. What do we mean by analysis of algorithms? Why do we care? Some simple examples.

2. Mathematical background and some useful mathematical techniques. Orders of growth of functions. Solving and estimating solutions of recursions. Generating functions. Probabilistic notions and techniques.

3. Heapsort and Quicksort. v

4. Hashing.

5. Binary search trees.

6. Dynamic programming.

7. Greedy algorithms.

8. Amortized analysis.

9. Graph algorithms; in particular, depth-first search and some of its remarkable applications.

10. The theory of NP-completeness.

There are many other topics that I'd really like to cover as well. This is just a fascinating field. We'll see…

There will be one homework assignment each week. I will not accept assignments handed in late.

There will be one or two in-class "mid-term" exams, and one final exam.

All the exams will be "closed-book" exams.

This course does not involve any programming per se, although without a doubt your experiences in building serious programs will help you understand many of the issues we deal with.

In fact, the course could well be regarded as a mathematics course. I will be proving things in class, and you will be expected to write formal proofs in your assignments and on exams. If this is something you are not ready to come to grips with, you should wait until you are ready to take this class.

There is a style to writing proofs. In fact, there are several styles. Your goal should be to write proofs that are easy to read and that illuminate the reason why something is true. This is not easy to do. Good writing of any kind is difficult, and we will work hard at it all term.

Probably the single most important proof technique in this area is mathematical induction. I will assume not only that you are familiar with this, but are comfortable using it. I will not teach it, but I will expect to see inductive proofs written out clearly and well.

I also expect you to be familiar with standard mathematical notations such as summations (and of course, integrals). Some of this is reviewed in Appendix A of the text. I will not review this in class. I expect you to know it, and we will be using it a lot.

One thing is very important to bear in mind: like any other kind of writing, a proof must be understandable. If I can't understand what you are writing, then it can't be correct. And I'm not going to try to guess what you had in mind. If you are uncertain how to express something, please just talk to me or send me email, and I'll try to help. But don't even bother writing something that can't be understood.

Think of this like you would when writing a computer program. If the compiler or interpreter can't understand it, it's wrong. And you have to be really careful with your use of language and terms. For instance, one thing beginning programmers often get mixed up about is the correct use of "or" and "and". The meaning in computer languages is not the same as in English (or any other natural language, so far as I know). The same is true in proofs. We use language in very precise and fixed ways in proofs, and we do this so that what we write can be understood in its exact meaning by anyone at any time, anywhere in the world.

Just for a simple example: the sentence "All horses are not white." does not mean the same as "Not all horses are white." At least, not when writing proofs. In ordinary English, these two sentences are generally regarded as equivalent. But for our purposes they are not. You have to be careful about this.

Collaborating with Others

I encourage you to talk with other students—in fact, with anyone—about the topics we are covering. And I also enourage you to send me email with questions; I'll be happy to get back to you as quickly as I can. However, the writeups you hand in must be entirely your own. You may not copy proofs, or algorithms, or parts of proofs or algorithms, or anything else, from anyone else's paper, or from the web, or from books, or from anywhere else. And you must be able to explain to me what you have written.

Please do take this seriously. I'm very happy to try to help you out in person or by email. I really do want every one of you to succeed, and I'll try hard to make that happen. But I have no tolerance at all for plagiarism. If I find evidence of it, you will receive an F for the course. And I don't give "second chances".

Some University Policies:

• Student Conduct and Plagiarism

  Students are required to adhere to the University Policy on Academic Standards and Cheating, and to the University Statement on Plagiarism and the Documentation of Written Work, both of which can be found at http://www.umb.edu/admissions/ugrad_catalog/plagiarism.html, and also to the Code of Student Conduct, available online at http://www.umb.edu/student_affairs/code.html.

• Accommodations for Students with Disabilities

  Section 504 of the Americans with Disabilities Act of 1990 offers guidelines for curriculum modifications and adaptations for students with documented disabilities. If applicable, students may obtain adaptation recommendations from the Ross Center for Disability Services, M-1-401, (617-287-7430). The student must present these recommendations and discuss them with each professor within a reasonable period, preferably by the end of Drop/Add period.