1. Eulerian Cycles in directed graphs
Network Optimization
Eulerian Cycles in directed graphs
Get ahold of a network, and use the same network to illustrate the shortest path problem for communication newtorks, the max flow problem, the minimum cost flow problem, and the multicommodity flow problem. This will be a very efficient way of introducing the four problems. (Perhaps under 10 minutes of class time.)
James Orlin

2. The initial network 2 3 1
Every node has the same number of arcs coming in as going out. 4 5 6 9 7 8 10 11 12 15 13 14

3. Determine a tree directed into node 12 3 1
Determine a bfs (or dfs) tree directed into node 1. 4 5 6 9 7 8
In the tree, each node has one arc coming out except node 1. 10 11 12 15 13 14

4. Order the arcs coming out of each node2 3 1
The tree arc out of node j should be the last arc of A(j) 4 5 6 9 7 8 10 11 12 15 13 14

5. Create the walk Start at node 1 and create a walk.2 3 1
Start at node 1 and create a walk. 4 5 6 9 7 8
Visit nodes of A(j) in order. 10 11 12 15 13 14

6. Continue the walk Continue the walk. Visit nodes of A(j) in order. 2 31
Continue the walk. 4 5 6 9 7 8
Visit nodes of A(j) in order. 10 11 12 15 13 14

7. Continue the walk Continue the walk. Visit nodes of A(j) in order. 2 31
Continue the walk. 4 5 6 9 7 8
Visit nodes of A(j) in order. 10 11 12 15 13 14

8. Continue the walk Continue the walk. Visit nodes of A(j) in order. 2 31
Continue the walk. 4 5 6 9 7 8
Visit nodes of A(j) in order. 10 11 12 15 13 14

9. 15.082J / 6.855J / ESD.78J Network Optimization
MITOpenCourseWare
15.082J / 6.855J / ESD.78J Network Optimization
Fall 2010
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