$6\mathrm{.}25.$ Networks with node capacities. In some networks, in additjon to arc capecities, each

node $i,$ other than the source and the sink, might have an upper bound, say $w(i),$ on

the flow that can pass through it$.$ For example, the nodes might be airporis with limited

runway capacity for takeoff and landings, or nuight be switches in a communication

network with a limited number of ports. In these networks we are interested in deter$-$

mining the maximum flow satisfying both the arc and node capacities. Transform this

problem to the standard maximum fow problem. From the perspective of worst$-$case

complexity, is the maximum flow problem with upper bounds on nodes more difficult.

to solve than the standard muximum flow problem?