Have/Want List Matching Algorithm

Question

Have/Want List Matching Algorithm

I am implementing an item trading system on a high-traffic site. I have a large number of users that each maintain a HAVE list and a WANT list for a number of specific items. I am looking for an algorithm that will allow me to efficiently suggest trading partners based on your HAVEs and WANTs matched with theirs. Ideally I want to find partners with the highest mutual trading potential (i.e. I have a ton of things you want, you have a ton of things I want). I don't need to find the global highest-potential pair (which sounds hard), just find the highest-potential pairs for a given user (or even just some high-potential pairs, not the global max).

Example:

User 1 HAS A,C WANTS B,D

User 2 HAS D WANTS A

User 3 HAS A,B,D WANTS C

User 1 goes to the site and clicks a button that says 
  "Find Trading Partners" and the top-ranked result is
   User 3, followed by User 2.

An additional source of complexity is that the items have different values, and I want to match on the highest valued trade possible, rather than on the most number of matches between two traders. So in the example above, if all items are worth 1, but A and D are both worth 10, User 1 now gets matched with User 2 above User 3.

A naive way to do this would to compute the max trade value between the user looking for partners vs. all other users in the database. I'm thinking with some lookup tables on the right things I might be able to do better. I've tried googling around, since this seems like a classical problem, but I don't know the name for it.

Can anyone recommend a good approach to solving this problem? I've seen sites like the Magic Online Trading League that seem to solve it in realtime.

Answer 1

You could do this in O(n*k^2) (n is the number of people, k is the average number of items they have/want) by keeping hash tables (or, in a database, indexes) of all the people who have and want given items, then giving scores for all the people who have items the current user wants, and want items the current user has. Display the top 10 or 20 scores.

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[Edit] Example of how this would be implemented in SQL:

-- Get score for @userid wants
SELECT UserHas.UserID, SUM(Items.Weight) AS Score
FROM UserWants
INNER JOIN UserHas ON UserWants.ItemID = UserHas.ItemID
INNER JOIN Items ON Items.ItemID = UserWants.ItemID
WHERE UserWants.UserID = @userid
GROUP BY UserWants.UserID, UserHas.UserID

This gives you a list of other users and their score, based on what items they have that the current user wants. Do the same for items the current user has the others want, then combine them somehow (add the scores or whatever you want) and grab the top 10.

Answer 2

This problem looks pretty similar to stable roomamates problem. I don't see any thing wrong with the SQL implementation that got highest votes but as some else suggested this is like a dating/match making problem similar to the lines of stable marriage problem but here all the participants are in one pool. The second wikipedia entry also has a link to a practical solution in javascript which could be useful