The document discusses the maximal flow technique in a network aimed at optimizing the flow from a source node to an output node. It highlights a practical application in Durham, North Carolina, where the closure of Interstate 85 requires engineers to assess alternative routes for managing 6,000 cars per hour during repairs. This scenario exemplifies the application of maximal flow problems to real-world traffic management challenges.

1. Maximal Flow Technique
NETWORK

2. • In a network with one source node (point of
entry) and one output node ( point of exit)
• The maximal-flow problem seeks to find the
maximal flow
• Whether it be in cars, planes, fluids or electricity
• Which can enter the network at the source
node, flow through it, and exit at the output
mode in a given period of time

3. A highway capacity problem
• Durham, North Carolina
• Normally the north to south traffic around
Durham would use Interstate 85
• But the 1-85 will be out of commission for
extensive road repair for 2 weeks
• The north carolina highway commission
engineers need to find out whether alternative
routes will safely handle the 6,000 cars an hour
that normally use 1-85 going south