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What is the significance of residual graph in the context of network flow algorithms?
In network flow algorithms, the residual graph shows the remaining capacity of edges after flow has been sent through them. It helps to find additional paths for flow and determine the maximum flow in a network.
What is the significance of the residual graph in the Ford-Fulkerson algorithm for finding maximum flow in a network?
The residual graph in the Ford-Fulkerson algorithm shows the remaining capacity for flow in the network after some flow has been sent. It helps determine the path for additional flow to maximize the total flow in the network.
What is a residual graph and how is it used in the context of network flow algorithms?
A residual graph is a graph that represents the remaining capacity of edges in a flow network after some flow has been sent through it. In the context of network flow algorithms, the residual graph is used to find additional paths for flow to reach the destination by identifying edges with available capacity. This helps optimize the flow of resources through the network.
What is the maximum flow that can be achieved in a network with lower bounds on the flow of each edge?
In a network with lower bounds on the flow of each edge, the maximum flow that can be achieved is the total flow that satisfies all the lower bounds on the edges while maximizing the flow from the source to the sink.
How can residual network flow be optimized to improve the efficiency of transportation systems?
Residual network flow can be optimized in transportation systems by adjusting the flow of traffic to minimize congestion and delays. This can be achieved through better route planning, traffic signal coordination, and real-time monitoring to make adjustments as needed. By optimizing the flow of traffic, transportation systems can operate more efficiently and reduce travel times for commuters.
