Consider the following generalization of the maximum flow problem.
you are given a directed network g = (v; e) with edge capacities fceg. instead of a single (s; t)
pair, you are given multiple pairs (s1; t1); (s2; t2); : : : ; (sk; tk), where the si are sources of g and the
ti are sinks of g. you are also given k demands d1; : : : ; dk. the goal is to nd k flows f(1); : : : ; f(k)
with the following properties:
f(i) is a valid flow from si to ti.
for each edge e, the total flow f(1)
e + f(2)
e + + f(k)
e does not exceed the capacity ce.
the size of each flow f(i) is at least the demand di.
the size of the total flow (the sum of the flows) is as large as possible.
how would you solve this problem?