W07/CS592
Homework Five
Design and Analysis of Algorithms
Due: Apr. 17, Tuesday, 2007
There are 4 problems
1.
Page 577, Problem 234 (a)(b).
Alternative minimumspanning tree algorithm
In this problem, we give pseudocode for three different algorithms. Each one
takes a graph as input and returns a set of edges T. For each algorithm, you must
either prove that T is a minimum spanning tree or prove that T is not a minimum
spanning tree. Also describe the most efficient implementation of each algorithm,
whether or not it computes a minimum spanning tree.
(a)
MAYBEMSTA(
G
,
w
)
1
sort the edges into nonincreasing order by their weights
w
2
T
←
E
3
for
each edge
e
, taken in nonincreasing order by weight
4
do if
T – {
e
} is a connected graph
5
then
T
←
T –{
e
}
6
Return
T
7
End
(b)
MAYBEMSTB(
G
,
w
)
1
T
←
φ
2
for
each edge
e
, taken in arbitrary order
3
do if
T
∪
{
e
}has no cycles
4
then
T
←
T
∪
{
e
}
5
Return
T
6
End
2.
(The widest path problem)
Let
P
(
u
,
v
) be a path from vertex
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 Winter '05
 Shen
 Algorithms, Graph Theory, Shortest path problem, Dijkstra, widest path, widest path problem

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