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QLDGeneral MathematicsQuick questions
Unit 4: Investing and networking
Quick questions on Flow networks, maximum flow and minimum cut (QCE General Mathematics Unit 4)
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are flow networks?Show answer
A flow network is a directed graph with a single source (where flow starts) and a single sink (where flow ends). Each edge has a capacity, the maximum flow it can carry in the direction of its arrow. The flow along any edge cannot exceed its capacity, and at every intermediate vertex the flow in must equal the flow out (nothing is created or stored).
What is maximum flow by inspection?Show answer
The maximum flow is the largest total that can travel from source to sink while respecting every capacity. On a small network you find it by inspection: trace paths from source to sink, send as much as the smallest capacity on each path allows, reduce the remaining capacities, and repeat with other paths until no more flow can be pushed through. The total sent is the maximum flow.
What is the maximum-flow minimum-cut theorem?Show answer
The theorem states that the maximum flow from source to sink equals the capacity of the minimum cut, the cut with the smallest capacity. This gives a powerful method: find the minimum cut, and its capacity is the maximum flow. On larger networks where inspection is hard, locating the bottleneck cut is the reliable way to confirm the answer.
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