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CSE5211/4081 Analysis of Algorithms
Fall 2010
Test 3
(
Six
Questions, answer double sided
)
Points Grad 65/ UG 60
Key below.
Q1.
LUP decomposition:
1a (Grad 6, UG 10):
decompose the matrix [row1, row2, row3]
[4
-5
6
,
8
-6
7
,
12
-7
12]
(Text exc 28.1-2)
1b (Grad only, 4):
Solve the corresponding equations from your
decomposed LU
matrices
. Consider right hand side b=[0, 0, 0]
Looking for pivoting.
Rest are updating row-cols. Corner elements by A’-vw^T/a11
1b. Right hand causes trivial solutions, e.g., 0,0,0. Almost any answer is accepted as long
as it is attempted. Even though the solution is trivial, the process of solving using first L
and then U is important.
Always draw the corresponding graph before starting to answer.
Q2 (G, UG 10).
Draw a undirected G=( V={a, b, c, d, e}, E={((a,b), (b,c), (b,e), (b, d),
(c,e), (c,d) }. Find the articulation point in the graph using the respective DFS-based
algorithm. Show the steps of your computation (the DFS tree with appropriate node
numberings, etc.)
DFS pre-ordering number.
Then, “low” numbering, and using the condition to detect obvious articulation pt node