0
$\begingroup$

Given a set of buyers, houses, agents with the following constraints:

  1. Agents only know a subset of buyers
  2. Agents only know a subset of houses
  3. Agents can only do some amount of transactions

Construct a flow network to model the problem. Disclaimer this is homework

I have put together some thoughts on a solution to this problem. First I realized that agents should be right before the sink node with a max flow equal to the number of possible transactions. This would then limit the number of transactions that can flow through an agent since the max flow can't be exceeded.

I was then thinking that it would be possible to put an edge between each person and house that an agent knows (example if agent knows person A, B and house 1, 2 there are edges (A,1), (A,2), (B,1), (B,2)). Finally, connect each house that an agent knows to an agent with max flow of 1. Then by running a Ford-Fulkerson algorithm across it the inflow of the sink node would indicate max number of transactions.

However, I am concerned that there is no limit of stopping a house from being purchased more than once. I have tried building the network with various configurations (swapping houses and clients, building nodes of client/house pairs) and nothing seems to solve this specific problem.

I am mostly looking for hints to solve this problem.

$\endgroup$
1
$\begingroup$

Hint: think about your source node and what it is connected to.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.