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CMPSCI 611: Advanced Algorithms Micah Adler

Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 1 Out: September 24, 2001
Due: October 1, 2001
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. ([CLR] problem 32-1)
a) Show how to multiply two linear polynomials ax + b and cx + d using only three multiplications.
b) Give two divide-and-conquer algorithms for multiplying two polynomials of degree-bound n that
run in time (n log 3 ). The rst should divide the input polynomial coe∆cients into a high half and a
low half, and the second algorithm should divide them according to whether their index is odd or even.
2. In this question, we shall obtain a more exact bound on the running time of matrix multiplication, and


Source: Adler, Micah - Department of Computer Science, University of Massachusetts at Amherst


Collections: Computer Technologies and Information Sciences