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306
1 (C,S)
D
2
(G,2)
F
Solutions to Exercises
26. (a) Applying the first version of Dijkstra's algorithm to the digraph produces the labels shown. Only
the labels at
A
and
B
are correct. There is a negative weight cycle
HGJCIH
from which every
vertex except
A
and
B
is accessible. So, repeating the cycle various numbers of times before
heading to a vertex (except
A
or
B)
changes the labels of that vertex, so the labels on every vertex
(except
A
and
B)
are meaningless.
(b) This time BellmanFord does not help, because of the negative weight cycle.
C
1 (C,S)
D
(B,~
2
E
(J, 7)
2
(G,O)
F
27. [BB] As described in the text, the second last vertex on a shortest path is
p(j).
Since a shortest path
to
Vj
makes use of a shortest path to
p(j)
following by edge
p(j)Vj,
the third last vertex on a shortest
path to
Vj
is
p(p(j)),
this being the second last vertex on a shortest path to
p(j).
So the vertices of a
shortest path to
Vj,
in reverse order, are
Vj, p(j), p(p(j)), p(p(p(j))),
... ,
VI.
28. Yes it can. When
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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