General Mathematics · Unit 4 · Networks and decision mathematics 2 · Flow networks
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Water flows through a network of pipes from a reservoir (R) to a storage tank (S). The diagram shows the maximum flow rate (L/min) through each pipe. Determine the minimum cut capacity in the network.
A water distribution network connects a treatment plant (P) to four suburbs via interconnected pipelines. The diagram shows the maximum capacity (in megalitres per day) of each pipe. (a) Identify all possible cuts that separate the plant P from suburb D. (1 mark) (b) Determine the capacity of each cut. (1 mark) (c) State the minimum cut and explain what this represents for the network. (1 mark)
Which set of edges represents a cut that separates the source $s$ from the sink $t$ in the flow network shown?
The flow network diagram below shows a network with source $s$ and sink $t$. Which set of edges represents a valid cut that separates the source from the sink?
A water distribution network carries flow from a reservoir (R) to a treatment plant (T). The diagram below shows the maximum flow rate (kL/min) through each pipe. Which of the following sets of pipes forms a cut that separates the reservoir from the treatment plant?
A telecommunications network transmits data from a server (S) to a terminal (T) through a series of routers. The table shows the maximum data transmission rate (Mbps) through each connection between routers. (a) Construct a flow network diagram showing all vertices and directed edges with their capacities. (1 mark) (b) Identify two different cuts in the network and calculate the capacity of each cut. (2 marks) (c) Determine which of the two cuts you identified is the minimum cut. (1 mark)