CS E-124 -- Algorithms and Data Structures
Instructor: Michael Mitzenmacher
Course web page:
http://www.fas.harvard.edu/~libcs124/E124/class.html
Objectives
This course covers the modern theory of algorithms, focusing on the
themes of efficient algorithms and intractable problems. The course
goal is to provide a solid background in algorithms for computer
science students, especially those working in industry or planning to
continue on with further advanced coursework. I strongly encourage
mathematicians and people from other areas of study to take the course
as well.
Besides introducing the basic language and tools for algorithm
analysis, we will also cover several specific problems and general
design paradigms. Toward the end of the quarter, we will also examine
heuristic techniques often used in practice, even though in many cases
formal theoretical results are not known.
We will focus on the theoretical and mathematical aspects in class and
on the homework assignments. But because one gains a deeper
understanding of algorithms from actually implementing them, the
course will include a substantial programming component.
More details will be available when the first programming
assignment is given.
As you can see from the preliminary list of topics (included below),
we will be covering a great deal. I expect the course to be
challenging, both in terms of the workload and the difficulty of the
material. You should be prepared to do a lot of work outside of
class. The payoff will be that you will learn a lot of both useful
and interesting things.
Prerequisites
Students should be able to program in a standard programming language;
C, C++, or Java is preferred. Some mathematical maturity also will be
expected; students should have some idea of what constitutes a
mathematical proof and how to write one. Some knowledge of basic
probability will also be helpful. If you do not have sufficient math
background (such as Math E-104), you should reconsider taking this
course.
Assessment
Your performance will be measured in four ways. (The percentage
contributions to your grade given below are approximate and
subject to change.)
- Problem sets (30%): There will be 6-7 problem sets. They will
generally be due one week after they are given out. These sets will
primarily be mathematical and/or theoretical in nature. These
assignments are governed by the collaboration policy, given below.
- Programming assignments (20%): There will be 2-3 programming
assignments.
Generally you will have two weeks for programming assignments.
- Midterm Exam (20%): There will be one exam approximately 1/2 of the
way through the course.
- Final Exam (30%):
All assignments will be due on the
date assigned. Assignments will not be accepted late with the
exception of medical emergencies or similar exceptional circumstances
that must be discussed in advance with the instructor. Please remember
it is better to turn in an incomplete assignment rather than no
assignment.
Collaboration Policy
I would like to emphasize the rules on working with others on homework
assignments. For the programming assignments, in somce cases it may
be possible to work in pairs; this will be decided further in the
course. In such a case, it is assumed you will not work with
anyone besides your partner.
For problem sets, limited collaboration in planning and thinking
through solutions to homework problems is allowed, but no
collaboration is allowed in writing up solutions. You are allowed to
work with one or two other students currently taking E124 in
discussing, brainstorming, and verbally walking through solutions to
homework problems. But when you are through talking, you must write up
your solutions independently and may not check them against each
other. There may be no passing of homework papers between
collaborators; nor is it permissible for one person simply to tell
another the answer.
If you collaborate with one or two other students in the course in
the planning and design of solutions to homework problems, then you
should give their names on your homework papers.
Under no circumstances may you use solution sets to problems that
may have been distributed by the course in past years, or the
homework papers of students who have taken the course past years.
Nor should you look up solution sets from other similar courses.
Violation of these rules may be grounds for giving no credit for a
homework paper and also for serious disciplinary action.
Severe punishments will apply, so please do not violate these rules.
If you have any questions about these rules, please ask an instructor.
Required Text
There is no required text. I recommend, however, you
consider at least one of the following books:
- Introduction to Algorithms, by Cormen, Leiserson, Rivest, and Stein.
This book is probably worth buying if you are going to study
algorithms beyond this course. It is primarily a theoretical
text, and it is quite encyclopedic in nature. If you are looking
for help with the proofs and mathematics, this is a good book
to purchase.
- Algorithm Design, by Kleinberg and Tardos.
This is also an excellent book, with a different style. It follows
the course quite closely, but it is not as encyclopedic as the other
book, and in particular assumes a lot more background.
In place of a book, class notes will be regularly made available.
Generally these notes will not be available until a few days after
the corresponding lecture.
Class Information/Notes
Class notes, homework assignments, and other information will be made
available on the Web when possible. For access go to the class web
site. Generally this information will be available in Postscript, so
you will want to find a Postscript viewer. In many cases, the class
web-site may be the only location where information is posted or
available, so look in from time to time!
Incomplete List of Topics
- Fundamentals
- Induction
- Recurrence Relations
- Big-Oh and Little-Oh notation
- Merge-sort
- Graph Algorithms
- Depth-first search, strongly connected components
- Breadth-first search, Djikstra's algorithm
- Greedy Algorithms
- Minimum spanning tree
- Union find
- Set cover
- Huffman coding
- Dynamic Programming
- Longest common subsequence
- Traveling salesman
- Divide and Conquer
- Integer multiplication
- Matrix multiplication
- Fourier transforms
- Hashing
- Balls into Bins problems
- Bloom Filters
- Document Similarity
- Sorting and Searching
- Quicksort, bubblesort, insertion sort, etc.
- Binary search trees, B-Trees, Splay Trees
- BiSuffix trees
- Linear Programming
- Problem definitions and solution techniques
- Reductions
- Maximum matching
- Randomized Algorithms
- Primality testing and factoring, RSA
- Median-finding
- NP-completeness
- Basic NP-complete problems
- Branch and bound
- Approximation algorithms
- Simulated annealing
- Novel approaches to NP-completeness