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The advanced study of data structures and algorithms
and the mathematics needed to analyze their time and space complexity.
Text: Our text is Introduction to Algorithms, third
edition by Thomas H. Cormen, Charles E. Leiserson, Ronald
L. Rivest, and Clifford Stein. Another good reference is Algorithm Design by Kleinberg and Tardos
CS361 or an equivalent undergraduate algorithms class is a
prerequisite for this class. You should be familiar with the
following topics: asymptotic notation; recurrence relations and simple techniques for solving recurrences;
proofs and basic proof techniques such as induction; basic probability; basic logic; basic graph theory; and algorithms and data structures as covered in an
undergraduate class. If you have taken and done well in an undergraduate class that
uses our required textbook, or the textbook "Algorithm Design" by Kleinberg
and Tardos, then you should be ok. If not, then you should take
CS361 (and/or CS362) prior to taking this class.
- Assignments are due at the beginning of class on the due
date. Assignment deadlines are strict: late homeworks will
automatically receive a grade of zero, without prior
approval. Prior approval is generally given only in the case of a
medical problem or family emergency.
- Group collaboration is encouraged on the homeworks, provided that
you write at the top of your homework the names of all the other
students that you collaborated with. Note that although collaboration
is encouraged, the solutions must always be written up
individually. You should not look at or copy another student's
solution and should not copy solutions from the
Internet. In particular, when writing up your solutions, you should not
be looking at any other solution. A rough rule of thumb here is the ``Star Trek`` Rule. After working with your group,
go watch a half hour of Star Trek on TV, or your favorite mindless (sorry Trekkies) but fun TV show, before you write up the solutions.
You may consult other textbooks or the Internet as you would another student (i.e. cite your source and use the ``Star Trek'' rule).
Remember Copying solutions from another student or from the
Internet is cheating. In case a student presents a solution that
is essentially identical in whole or in part to solutions from another
student or other source, that student will receive a 0 on the
assignment, may be reported to the University Administration and may
not be permitted to continue in the class.
- Put pages of hw in order. We don't care what order you
solve the hw in, but before you turn it in, you must put the problems
in order (this makes grading much easier)
- Staple hws, do not use paper clips, folding, tape, putty,
gum, etc. Prof Saia and the TA do not bring staplers to class, so
make sure you staple the hw before class (stapling helps us keep
together all pages of your hw)
- Regrades: if you feel a mistake was made grading your hw, please
let the TA know about it (if you still feel there is a problem, then
please talk to Prof. Saia). Please ask for a regrade within one week
of receiving the graded assignment.
Notes on Grading Hws
Your hws and test answers should have the following properties. We will be looking for
these when we grade:
- Clarity: Make sure all of your work and answers are clearly
legible and well separated from other problems. If we can't read it,
then we can't grade it. Likewise, if we can't immediately find all of
the relevant work for a problem, then we will be more likely to grade
only what we see at first.
- Completeness: Full credit for all problems is based on both
sufficient intermediate work (the lack of which often produces a
'justify' comment) and the final answer. There are many ways of doing
most problems, and we need to understand exactly how YOU chose to solve
Here is a good rule of thumb for deciding how much detail is sufficient:
if you were to present your solution to the class and everyone understood
the steps, then you can assume it is sufficient.
- Succinctness: The work and solutions which you hand-in should be
long enough to convey exactly why the answer you get is correct, yet
short enough to be easily digestible by someone with a basic knowledge
of this material.
If you find yourself doing more than half a page of dense algebra,
generating more than a dozen numeric values or using more than a page
or two of paper per problem for your solution, you're probably doing
too much work.
Don't turn in pages with scratch work or multiple answers - if you need to
do scratch work, do it on separate scratch paper. Clearly indicate your
final answer (circle, box, underline, etc.).
Note: It's usually best to rewrite your solution to a problem before you
hand it in. If you do this, you'll find you can usually make the
solution much more succinct.
Topics will likely include:
- Probability and Expectation: linearity of expectation, birthday paradox, coupon collector's problem. Applications: Hashing, Quicksort, Bucketsort, Skip Lists, maybe Rabin-Karp Algorithm? (fingerprinting) (2.5 weeks, Chapter 5)
- Divide and Conquer: Recurrence Relations, Annihilators, Recursion and Strong Induction (2 weeks, Chapter 3 and 4 and notes; Chapters 6 and 12)
- Dynamic Programming: String Alignment, Matrix Multiplication, Longest Common Subsequence (1.5 weeks, Chapter 15)
- Greedy Algorithms (1 week, Chapter 16)
- Amortized Analysis: Dynamic Tables and Union Find (1 week, Chapter 17)
- Graph Algorithms with Proofs: Minimum Spanning
Tree, Single-Source Shortest Path, All-Pairs Shortest Paths (2 weeks, Chapters
- Network Flow, Max Matchings, Min-cut Max-flow (2 weeks, Chapter 26)
- Linear Programming and Duality (1 weeks, Chapter 29)
- Fast Fourier Transform, Shor's Algorithm (~1 week (time permitting), Chapter 30)
- NP-Hardness and Approximation Algorithms (2 weeks , notes)
- Homeworks, 20% (6-8)
- Midterm, 40%
- Final, 40%
"No deals, Mr. Bond.": Grades assigned at the end of the semester are final. You will not be able to do any additional projects, papers, etc. to change your grade.