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74
Chap. 11 Graphs
23456
11013126 2
2
351
61
2
3
8
15 15
41
1
1
0
53
11.16
The problem is that each entry of the array is set independently, forcing pro
cessing of the adjacency list repeatedly from the beginning. This illustrates
the dangers involved in thoughtlessly using an inef
f
cient access member to a
data structure implementation. A better solution is to process the actual edges
within the graph. In other words, for each vertex, visit its adjacency list. Set
the shortestpaths array by setting the values associated with that edge. If the
array is initialized with values of
∞
, then any vertices not connected by an
edge will retain that value.
11.17
Clearly the algorithm requires at least
Ω(
n
2
)
time since this much informa
tion must be produced in the end. A stronger lower bound is dif
f
cult to
obtain, and certainly beyond the ability of students at this level. The primary
goal of this exercise is for the students to demonstrate understanding of the
concept of a lower bound on a problem, in a context where they will not be
able to make the lower bound and the algorithm’s upper bound meet.
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 Fall '08
 BELL,D

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