The Design and Analysis of Algorithms

Computer Science 681
Fall 2003


Here is the take-home final. It is due Friday Dec 12th at 4pm, unless  you confirmed alternate arrangements by email before December 5th.  Here is the same final in pdf format.

You can drop the final off in my office (5153 Upson). You can leave it under my door, if I am not here.

FAQ for the final:

Office Hours During the Final week

Instructor: Éva Tardos

5153 Upson
eva at
Regular Office Hours: Wednesdays 1:30-2:20 and Fridays 10:30-11:30

TAs: Chaitanya Swamy                              Tom Wexler

        5136 Upson                                                            4106 Upson                                                                     
        255-0226                                                               255-8758                     
        swamy at                                           wexler at
        Regular Office Hours Tuesdays 3-4                          Regular Office Hours Thursdays 2-3

Time: MWF 2:30-3:20 pm.

Place: 306 Hollister Hall

Handouts and Announcements


CS 681 is an introductory graduate-level course on algorithms. Although we will be covering a number of current research topics in the design and analysis of algorithms, the primary focus will be on principles in algorithm design that are conceptually clean and broadly applicable. Our goal is to make the course both accessible and useful for graduate students in any area that makes use of algorithms.

Some of the broad areas we will be considering are: basic graph algorithms and data structures from a current perspective; the use of randomization; intractable problems and the design of approximation algorithms; and fundamental techniques from combinatorial optimization. We will be looking at algorithms as they appear in a variety of settings; some of these may include communication networks, on-line algorithm, computational geometry, computational biology, and the design of error-correcting codes.


There is no specific course pre-requisite, though knowledge of some material at the level of an undergraduate algorithms course, such as CS 482 will be assumed at various times. In particular: elementary data structures and elementary algorithms, such as basic sorting and searching, basic graph terminology, and basic graph algorithms, such as graph search, asymptotic order of growth notation, and basic recurrence relations for analyzing algorithms. It will also be helpful to have seen basic definitions of probability (e.g. random variables and their expectations), as well as some very basic linear algebra.

The course will follow the same basic outline, with a similar set of topics as CS482. However, the actual overlap with 482 will be rather minimal, as all topics will be covered at a more advanced level.



Homework will be assigned every 1-2 weeks; it should be handed in in lecture, at the end of class, on the day it is due.

Late homeworks will not receive credit. (If a genuine emergency situation prevents you from handing in an assignment on time, come talk to me and we can work something out.)

You are expected to support the answers to the homework with proofs. Much of the homework will consist of questions asking you to design algorithms for various problems. A complete answer consists of a clear description of an algorithm (an English description is fine), followed by an analysis of its running time and a proof that it works correctly; you do not need to implement the algorithm. You should try to make your algorithms as efficient as possible.

You may discuss the homework problems with other members of the class, but you must write up the assignment separately and list the names of the people with whom you discussed the assignment.


There will be take-home exams for mid-term and final. Unlike the homework assignments, these must be done completely on your own.


The homework will count for 50% of the grade, the mid-term for 20%, and the final for 30%.


We will use two books throughout the course. The main textbook will be

In the first few weeks we will follow the book:

Some other useful books are