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Engineering
xercises
2. How would you modify your algorithm in the last
Exercises
1. Describe (in words) an algorithm for finding
k
edge
isjoint paths joining a given pair of vertices in a
problem to find a set of
k
vertexdisjoint paths (a set
of paths is vertexdisjoint if no vertex appears on
more than one path – excepting the initial and final
vertices in the path).
disjoint paths joining a given pair of vertices in a
directed graph. (A set of paths is edgedisjoint if no
edge appears in both paths).
Let s and t be the given pair of vertices. Treat the graph as
flow network with all edges having capacity 1 Now find
We can use the same approach to find vertexdisjoint
paths. We first must create a new graph having vertices
u
1
, u
2
for each vertex u in the original graph. For each
pair u
1
, u
2
, we include an edge (u
1
,u
2
) and for each edge
v in the original graph we add an edge (u
v
in the
a flow network with all edges having capacity 1. Now find
a maximum flow in the graph from s to t. If the capacity of
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 Spring '09
 BUHLER
 Algorithms

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