1
CSE 421
Algorithms
Richard Anderson
Lecture 24
Network Flow Applications
Today’s topics
•
Problem Reductions
– Undirected Flow to Flow
– Bipartite Matching
– Disjoint Path Problem
• Circulations
•
Lowerbound constraints on flows
•
Survey design
Problem Reduction
•
Reduce Problem A to Problem B
– Convert an instance of Problem A to an instance
Problem B
– Use a solution of Problem B to get a solution to
Problem A
• Practical
– Use a program for Problem B to solve Problem A
• Theoretical
– Show that Problem B is at least as hard as Problem A
Problem Reduction Examples
•
Reduce the problem of finding the
Maximum of a set of integers to finding the
Minimum of a set of integers
Find the maximum of:
8,
3,
2,
12, 1, 6
Construct an equivalent minimization problem
Undirected Network Flow
•
Undirected graph with edge capacities
•
Flow may go either direction along the
edges (subject to the capacity constraints)
u
s
t
v
10
10
5
20
20
Construct an equivalent flow problem
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 Fall '06
 RichardAnderson
 Algorithms, Graph Theory, Shortest path problem, Bipartite graph, Maximum flow problem, Network flow, edge disjoint paths

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