Engineering
xercises
2. Identify an augmenting path in the bipartite graph shown below,
Exercises
1. Consider the weighted bipartite graph shown below.
relative to
the matching defined by the
heavy weight edges.
a
b
d
e
The path daebfc is an augmenting path.
a
b
d
e
4
3
2
5
3
2
c
f
Construct the flow graph used to find a max weight matching in
this graph and find a mincost flow corresponding to a max wt
matching.
Show the matching obtained using this augmenting path.
c
f
1

a
b
d
e
a
b
d
e
4
3
2
5
3
2
s
t
all capacities are 1
source/sink edge
c
f
The heavyweight edges correspond to a mincost flow. The weight of the
corresponding matching is 10.
c
f
1
costs are zero
11
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View Full DocumentEngineering
3. The figure below shows two matchings in a graph.
4. As described in the notes, the augmenting path algorithm
,g
g
p
g
performs a lot of redundant work each time it starts a new
augmenting path search. Describe a version that would eliminate
much of this overhead.
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 Spring '09
 BUHLER
 Algorithms, Bipartite graph, path search

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