Power in Unity:Forming Teams in Large-Scale

Community Systems

Aris AnagnostopoulosS, Luca BecchettiS,Carlos CastilloY, Aris GionisY, Stefano LeonardiS

YYahoo! Research – SSapienza University of Rome

2 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Outline

• Motivation

• Problem definition

• Algorithms

• Experiments

Wikipedia Category: Heist films

1960 2001

4 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Do you have ...?

• ... too many papers/proposals to review?

• ... too many interviews to do?

Review workload forlast year: ~60 papers

5 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Motivation

• Staff of people with different skills

• Stream of tasks arriving online

• Create teams on-the-fly for each task

– Teams should be fit for the tasks– Allocation should be fair to people

6 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Criteria

• Fitness

– e.g. if fitness is success rate, maximize expected number of successful tasks

• Fairness

– everybody should be involved in roughly the same number of tasks

Trade-offs may appear: do you see how?

7 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Framework

Jobs/Tasks k

People n

Skills m

Teams k

Score/fitness

Load

8 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Properties

• Pareto-dominant profiles

• Non decreasing performance

• Job monotonicity

• Non-increasing marginal utility

9 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Properties (cont.)

• Non decreasing performance

– c.f. Brooks' Law: “adding manpower to a late software project makes it later”

• Job monotonicity

– May not hold e.g. start from unfeasible task

• Non-increasing marginal utility

– May not hold e.g. if all skills are required

10 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Team profiles

• Maximum skill

• Additive skills

• Multiplicative skills

• Binary profiles

– All of the above are equivalent

11 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Score functions

• Fraction of skills possessed

• is sub-modular: greedy method provides an approximation within a constant factor

• In other applications e.g. Ocean's 11, all skills are required: covering problem

12 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Balanced task covering

• Cover all the tasks

• Objective

• NP-hard problem even with k = 2

– Reduction from MSAT• People = variables; Skills = clauses;

• People in team 1: TRUE, People in team 2: FALSE

• Maximum load of 1 is achieved if clauses satisfied

• Offline setting has a randomized approx. algo. that succeeds with prob 1-± with ratio

13 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Balanced task covering - Online

• Evaluate by competitive ratio

– Compare with optimal offline assignment

• Basic algorithms

– Assemble the team of minimum size– Assemble the team that keeps the maximum

load of a person low

• Competitive ratios are bad:

14 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Weighted set cover

• Weight each set by

– Competitive ratio

• Weight each set by

– Competitive ratio

Experiments

16 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Datasets

Mapping of data to problem instances

Summary statistics

17 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Results (center)

18 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Results (center)

19 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Results (most loaded users)

20 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Results (most loaded users)

21 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Related works

• Lots of works on matching and scheduling problems

• Lots of works on finding one expert

– IR-style and SN-style

• T. Lappas, K. Liu, E. Terzi. Finding a team of experts in social networks, KDD'09.

– Focuses on communication costs

22 Power in Unity – Anagnostopoulos, Becchetti, Castillo, Gionis, Leonardi

Future works

• Building, retrieving and ranking complex information elements

– document/answer sets, photo sets, geo points, RDF sub-graphs, etc.

• Algorithms to support massive collaboration

– decisions, coordination, awareness, etc.

Buddy Venturanza @ Flickr (Creative Commons)

Thank you!