On Efficient Recommendations for Online Exchange Markets.

1. On Efficient Recommendations for Online Exchange Markets. Zeinab Abbassi, Laks V. S. Lakshmanan: ICDE 2009:712-723

2. Motivation peerflix.com- exchange movies readitswapit.co.uk- exchange books oddshoe.org- exchange shoes Applications on online social networks like Facebook.

3. Problem definition Simple exchange market- restricted to a set of swap recommendations Exchange markets with short cycles- short exchange cycles of up to length k Probabilistic exchange markets- probability associated with each user engaged in the transaction Optimize the number of items exchanged.

4. Cycle Covers Cycle cover problem: Given a graph and a subset of marked elements (nodes or edges) find a minimum length set of cycles whose union contain all the marked elements. ExchangeMarket problems can be modeled as a cycle cover problems.

5. Recommender systems Content based- user will be recommended items similar to the ones the user preferred in the past Collaborative- The user will be recommended items that people with similar tastes and preferences liked in the past • Hybrid approaches: combination of both methods

6. Kidney Exchange problem similar to simple market exchange. If exchanges are restricted to swaps, can be solved using maximum weighted perfect matching.

7. Model Assumptions Algorithm for generating exchange cycles is run periodically User accounts, item lists and wish lists are updated User does not own multiple copies of an item and does not wish for multiple copies of an item. Set of feasible exchanges changes with time

8. Simple Exchange Market Given a set of users U with the item lists Su and wish lists Wu for each user u ∈ U, find pairs of users such that items on the item list of one user appear on the wish list of another user.

9. Alice Bob B7 Alice Bob B1

10. Exchange markets through short cycles If we restrict ourselves to swaps, none of the users may be satisfied. Find an optimal set of conflict-free cycles of length < k

12. Probabilistic exchange markets • Let Pu(v) denote the probability that u is willing to do an exchange with user v, and let Qu(i, j) be the probability that user u will exchange item i with item j. • Probability of a cycle = Pu1 (u2) × Qu1 (i1, ik) × Pu2 (u3) × Qu2 (i2, i1) . . .×Puk (u1) × Quk (ik, ik−1). • Our goal is to find a set of conflict-free cycles that maximize the total expected number of items exchanged.

13. Approximation algorithms The Simple Market problem, the probabilistic market problem and the Kidney exchange problem for cycles of length > 2 are NP-Complete. A heuristic algorithm and three approximation algorithms have been developed which use a directed graph representation

15. A. Finding a maximal set of cycles

16. B. Greedy Algorithm

17. C. Local Search

18. D. Greedy/Local Search Run the greedy algorithm to find a set of cycles B and then run the local search algorithm starting from cycles in B.

19. Analysis |B|: number of cycles found OPT: weight of the optimal solution k : maximum length of a cycle

20. Experiments Algorithms implemented using MATLAB and tested using synthetic data sets. Performance of Maximal is comparable to others and is by far the most efficient.

21. Future work Investigations on real data sets Further exploration of probabilistic exchange markets Analysis of exchange markets which award points for giving away items which can be redeemed later when another user needs them.

22. Other directions Another research direction is to suggest recommendations which improve user experience by helping users find surprisingly good items. Zeinab Abbassi, Sihem Amer-Yahia, Laks V. S. Lakshmanan, Sergei Vassilvitskii, Cong Yu: Getting recommender systems to think outside the box. RecSys 2009: 285-288

23. Questions