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On Efficient Recommendations for Online Exchange Markets. Zeinab Abbassi, Laks V. S. Lakshmanan: ICDE 2009:712-723. M otivation. peerflix.com- exchange movies readitswapit.co.uk- exchange books oddshoe.org- exchange shoes Applications on online social networks like Facebook.

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On efficient recommendations for online exchange markets

On Efficient Recommendations for Online Exchange Markets.

Zeinab Abbassi, Laks V. S. Lakshmanan: ICDE 2009:712-723


M otivation
Motivation

peerflix.com- exchange movies

readitswapit.co.uk- exchange books

oddshoe.org- exchange shoes

Applications on online social networks like Facebook.


Problem definition
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.


Cycle covers
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.


Recommender systems
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


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

matching.


Model
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


Simple e xchange market
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.


Alice

Bob

B7

Alice

Bob

B1


Exchange markets through short cycles
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


Probabilistic exchange markets
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.


Approximation algorithms
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





D greedy local search
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.


Analysis
Analysis

|B|: number of cycles found

OPT: weight of the optimal solution

k : maximum length of a cycle


Experiments
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.


Future work
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.


Other directions
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



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