During a peak usage period following a power outage, the network of a community center began operating using packet switching, where data is divided into small packets and transmitted across the network, and bandwidth is provided on demand.
The infrastructure is composed of devices interconnected by links with limited capacities. Each link has a maximum transmission capacity in (MB/s), representing how much data can be transmitted. The main objective of the system is to maximize the total flow of data (packets) sent from S to T.
Since packets can follow different paths to reach the destination, the network can be modeled as a directed graph. To ensure the best possible performance, we aim to determine the maximum flow of packets that can be transmitted from the source to the destination. A schematic drawing of the community center's network with capacities is given below.
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