 
Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 1 Out: September 23, 2003
Due: September 30, 2003
Notes: On homework assignments, you are allowed to discuss the questions with a small number of other
people in the course. However, the emphasis of such discussions should be obtaining a solid understanding
of the solutions to the assigned problem. Thus, you must destroy any notes from your discussions, and then
write up the solutions on your own. For each problem, you must also list anyone you discussed that problem
with (even brie
y). You also must describe any other references you used.
The homeworks are due at the beginning of class on the due date. Late submissions will be accepted only
with special permission. Also, please take the time to write clear and concise answers. Credit will be reduced
if answers are unclear or long winded.
All questions count for the same amount of credit, although some are harder than others. Some of the
questions may require quite a bit of thought, so I encourage you to start early.
1. In this question, we shall obtain a more exact bound on the running time of matrix multiplication, and
use this to determine at what value of n Strassen's algorithm starts to outperform the nave matrix
multiplication algorithm. In order to do so, we shall use the fact that the solution to the recurrence
relation
T (n) = aT
n
