I have a situation where in a group of people, every person is trading with multiple people and giving them some money. It can be visualised as a directed bipartite graph with
R as the total set of people. A directed edge from
r some money with weight
w which is the weight of the edge. Now I'm an auditing firm and want to make sure that the total amount given out by a person should be as close as possible to the amount received by him. I can limit each such transaction (implying I can reduce the weight of any edge in the graph). What is the best way to solve this approximately with the minimum restrictions required (in terms of actual amount)?
a -> 10 -> b b -> 10 -> c c -> 5 -> a
can be limited to
a -> 5 -> b b -> 5 -> c c -> 5 -> a
10 units of transactions