Supporting Top-K Item Exchange Recommendation in Large Online Community

Zhan Su, Anthony K. H. Tung, Zhenjie Zhang

Item Exchange: Pioneer Trail / Frontier Ville • The most popular social game on Facebook

Item Exchange: Pioneer Trail / Frontier Ville • Player needs items to finish tasks

Item Exchange: Pioneer Trail / Frontier Ville • Wish List: waiting for help from your friends

Item Exchange: World of Warcraft • Auction-based approach

Item Exchange: World of Warlord • Problems with Auction-based approach – Inflation: the players prefer to exchange instead of selling their weapons

Item Exchange: Real Item • A popular website in Chinese

Item Exchange: Service • Some item/service swap web sites: – http://www.swapcycle.co.uk/ – http://www.u-exchange.com/

Agenda of the presentation • • • • •

Problem Definition (5 mins) Exchange between 2 users (5 mins) General Recommendation (5 mins) Experiments (5 mins) Conclusion and Future Work (2 mins)

Exchange Model • Exchange Model Wish List Unneeded List

Price List

$1

$5

Wish List

$2

$10

Unneeded List

$8

$16

Wish List Unneeded List

Eligible Exchange Pair • Exchange Model Wish List Unneeded List

Price List

$1

$5

Wish List

$2

$10

Unneeded List

$8

$16

Wish List Unneeded List

Eligible Exchange Pair • Formal definition – Only between two users – The unneeded items are in the wish list of the other user (item matching) – The values of the exchange items are approximately the same. Specifically, the ratio between the value is between b and b-1. b=0.8

+

$16

$1

$18

$10

Top-K Exchange Recommendation • How to maximize the utility of the exchange – We aim to recommend exchange candidates with maximal value for each user, i.e. sum on the item prices – For Alice, the value of the exchange is $15. For Bob, the value of the exchange is $16

$16

+

$18

Top-K Exchange Recommendation • How to maximize the utility of the exchange – There’s no multiple exchange pairs on a single pair of user. Why? – We prove that there is always a dominating exchange pair, maximizing the utilities of both sides.

$16

+

$18

Research Target • System’s Perspective – Handling updates on the list in real time – High throughput of the system – Scalability of the system in terms of users Wish List Unneeded List Wish List Unneeded List

Price List

1$

5$

2$

10$

8$

16$

We’re only … • Recommendation only – There’s no automatic commitment of the exchange

• Exchange between 2 users only – Multi-party exchange chain is hard to find and even harder to proceed

• No currency used – Inflation issue

Agenda of the presentation • • • • •

Problem Definition (5 mins) Exchange between 2 users (5 mins) General Recommendation (5 mins) Experiments (5 mins) Conclusion and Future Work (2 mins)

Hardness result • NP-hardness on finding optimal exchange – In terms of the lengths of the lists – Polynomial reduction from Load Balancing

• Fortunately, – The number of items are usually bounded by a constant, e.g. every individual player in WoW has limited number of weapons in hand.

Polynomial-Time Approximation Scheme • Map the combinations onto the price axis $8

$2

Wish List Unneeded List Wish List Unneeded List

$10

$16

$18

Price List

$1

$5

$2

$10

$8

$16

Approximate Value Table • Join the Wish list of Bob and Unneeded list of Celina Wish List Unneeded List Wish List Unneeded List

• Approximate all combinations using Approximate Value Table (AVT)

Approximate Value Table Iteration 1: Paper ($2) $1 $2 $3 $4

$6

$9

Entry App. Value LB

$13

$19

LB Items

UB

$28

UB Items

Approximate Value Table Iteration 1: Paper ($2) {Paper} is added $1 $2 $3 $4

$6

$9

$13

$19

$28

Entry App. Value LB

LB Items

UB

UB Items

1

{Paper}

2

{Paper}

2

2

Approximate Value Table Iteration 2: Bike ($16) $1 $2 $3 $4

$6

$9

$13

$19

$28

Entry App. Value LB

LB Items

UB

UB Items

1

{Paper}

2

{Paper}

2

2

Approximate Value Table Iteration 2: Bike ($16) {Bike} is added $1 $2 $3 $4

$6

$9

$13

$28

$19

Entry App. Value LB

LB Items

UB

UB Items

1

2

2

{Paper}

2

{Paper}

2

19

16

{Bike}

16

{Bike}

Approximate Value Table Iteration 2: Bike ($16) {Paper, Bike} is added $1 $2 $3 $4

$6

$9

$13

$19

$28

Entry App. Value LB

LB Items

UB

UB Items

1

2

2

{Paper}

2

{Paper}

2

19

16

{Bike}

18

{Paper, Bike}

Approximate Value Table Entry App. Value LB

LB Items

UB

UB Items

1

9

8

{Hammer}

8

{Hammer}

2

13

10

{Ribbon}

10

{Ribbon}

3

19

18

{Hammer, Ribbon}

18

{Hammer, Ribbon}

Entry App. Value LB

LB Items

UB

UB Items

1

2

2

{Paper}

2

{Paper}

2

19

16

{Bike}

18

{Paper, Bike}

Linear scan the UB of one table

AVT v.s. Brute-Force • AVT is more effective when list length>8

Agenda of the presentation • • • • •

Problem Definition (5 mins) Exchange between 2 users (5 mins) General Recommendation (5 mins) Experiments (5 mins) Conclusion and Future Work (2 mins)

A Naïve Solution • Maintain two AVTs between every pair of user – Quadratic overhead on storage – Linear update cost in terms of user #

• How to improve? How to narrow down the search space? – Critical Item – Optimizations on Insertion – Optimizations on Deletion

Critical Item • Some items are necessary for eligible exchange – If you don’t have hammer and ribbon, you can never exchange with Celina – If you don’t want bicycle, you can never exchange with Celina Wish List Unneeded List

Insertion • When a new item is inserted into a list – Update critical items for the user. Stop if new item is not critical – Find the users with the critical items – Recalculate the optimal exchange between Alice and every candidate user Wish List Unneeded List Wish List Unneeded List

Not critical!

Deletion • Can we update the recommendation only? – No. It may affect the top-k recommendation of others

Wish List Unneeded List Wish List Unneeded List

Wish List Unneeded List

Deletion • To keep all recommendations optimal – Update every pair of user with valid critical items – Much more expensive than insertion

• How to avoid unnecessary re-calculation? – Maintain k’ > k pairs of optimal recommendations – When some recommendations disappear, just display the backup ones

Agenda of the presentation • • • • •

Problem Definition (5 mins) Exchange between 2 users (5 mins) General Recommendation (5 mins) Experiments (5 mins) Conclusion and Future Work (2 mins)

Simulation Setup • Basic parameters – – – – – –

Maximal Value: $10,000 Minimal Value: $10 Matching relaxation b: 0.8 (default) List length: 15 (default) Number of items: 1500 (default) Number of users: 30,000 (default)

• Item Distribution – Synthetic data: exponential distribution, Zipf distribution – Real data: Ebay auction data

Simulation Setup • Item/Price Distribution

Workload Generation • Workload: a sequence of updates – Initially, the database is empty – Uniform selection on the user – Pick up Wanted list or Unneeded list with equal probability – Pick up insertion or deletion operation – Randomly pick an item based on a specific distribution on the items – Add/Remove the item in the specific list

Dynamics of the Simulation • System is stable after the lists are almost full

Results on Simulation with Ebay data

Conclusion • Item exchange: an emerging business of huge market value • Top-K Item exchange problem • Database performance issue • General system engine to support updates

Future Work • Social Network • Item Priority • System Performance – Index Structure: bitmap – Transaction: Insertion of item groups