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
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:
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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!