CS 395 Algorithmic Techniques for Bioinformatics
Department of Electrical Engineering and Computer Science
Northwestern
University
Fall 2005
Problem Set #9
Due Time:
At the start of class on Tuesday, 11/29/2005.
Required Problems:
-
(20 points) Problem 10.1.
-
(40 points) Problem 10.2
-
(40 points) Find a tree with 6 leaves
x1, x2, x3, x4, x5, and x6 such that the pair-wise distances of these leaves
are as specified by the following matrix:
| |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
| x1 |
0 |
10 |
11 |
14 |
15 |
14 |
| x2 |
|
0 |
7 |
14 |
15 |
14 |
| x3 |
|
|
0 |
15 |
16 |
17 |
| x4 |
|
|
|
0 |
11 |
10 |
| x5 |
|
|
|
|
0 |
3 |
| x6 |
|
|
|
|
|
0 |
Extra Credit Problems:
-
(40
points) Find a tree with 6 leaves x1, x2, x3, x4, x5, and x6 such that the
pair-wise distances of these leaves are bounded by the following two
matrices:
| |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
| x1 |
0 |
13 |
13 |
8 |
10 |
14 |
| x2 |
|
0 |
6 |
9 |
20 |
24 |
| x3 |
|
|
0 |
9 |
20 |
23 |
| x4 |
|
|
|
0 |
15 |
18 |
| x5 |
|
|
|
|
0 |
9 |
| x6 |
|
|
|
|
|
0 |
| |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
| x1 |
0 |
10 |
9 |
4 |
8 |
10 |
| x2 |
|
0 |
4 |
7 |
17 |
20 |
| x3 |
|
|
0 |
5 |
16 |
20 |
| x4 |
|
|
|
0 |
12 |
15 |
| x5 |
|
|
|
|
0 |
5 |
| x6 |
|
|
|
|
|
0 |