CS 2420 – Fall 2011
Program 7– 30 points
Flow Graphs
Part 1
Given a directed graph with edges marked with capacity, find the shortest path (in term of number
of legs) from the source to the sink which has a positive (remaining) capacity.
In this case, there are several shortest paths. ABCD is one of them.
from B to C can only carry 2).
It can carry 2 (as the path
In the provided starter code, a path is stored in PathInfo as a string (of the vertices of the path) and
the capacity of the path. Feel free to modify the starter code as desired.
Part 2
For the graph, list a series of augmenting paths that produce the maximum flow in a network
graph. List the final flow that was obtained.
CS 2420 – Assignment 7
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In the graph above, one might list the paths:
ABEFD 2
ABFD 1
To get any more flow, one has to consider pushing flow back along an edge. Thus, we would add
AEBCD 2
Flow=5
This is the maximum flow that would be possible (as only five units can flow out of node A).
CS 2420 – Assignment 7
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To be more efficient than the example, you are expected to use the Edmonds-Karp heuristics
1. Pick the shortest augmenting path available (for efficiency)
2. Of all same length paths (in terms of number of legs), pick the largest-capacity path available
Using these heuristics, you would produce something similar to
ABCD 2
AEFD 2
ABFD 1
CS 2420 – Assignment 7
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