Homework Assignment #4 (revised)
CS 410/584 Algorithm Design & Analysis: Spring 2009
This assignment is due Wednesday, 13 May, at the beginning of class. You should work
alone on this assignment. However, you are free to discuss the problems on the class
mailing list. (Or you can send me email questions directly; please put โCS 584โ at the
beginning of the subject line.) Please put โ410โ or โ584โ on your paper, depending on
which section you are registered in.
Reading: Chapter 26.1-3; Chapter 28.1, 28.2, 28.4; Chapter 30; Chapter 32 intro, 32.1,
32.3, 32.4
Note: On any homework exercise where you are asked to give an algorithm, you must
also provide an English description of how it works and at least one example execution.
Exercises: 25.2-6 (5 points; no need for an example), 26.2-2 (10 points; show each
augmenting path you use and the final flow), 28.4-1 (10 points), 28.4-4 (20 points, 584
only. Hint: Do Exercise 4A first.), 30.2-2 (5 points; show the results of the recursive calls
of FFT.)
4A (10 points): Let A be the adjacency matrix for directed graph G. What does A2
represent (assuming Boolean matrix multiplication)? Show an example for a graph of at
least 5 nodes.
4B (10 points): Explain how you would evaluate x56 + x36 + x5 at a point using many
fewer than 55 multiplications.
4C (5 points): Prove that ฯ2rk = โฯ2rk+r.