 
Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 1 Out: September 26, 2000
Due: October 3, 2000
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), and 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 very 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. a) Show how to multiply two complex integers (i.e., numbers of the form a + bi, where i = p
1, and
a and b are integers) using only 3 integer multiplies.
b) Strassen's algorithm is based on a way of multiplying two 22 matrices using seven multiplications.
We might try to improve on this by developing a way to multiply two 4 4 matrices using less than
the obvious 64 multiplications. How small would the number of multiplies have to be in order to do
