mehdi kargar aijun an york university, toronto, canada discovering top-k teams of experts...

Mehdi KargarAijun An

York University, Toronto, Canada

Discovering Top-k Teams of Expertswith/without a Leader in Social Networks

Overview

• Team Formation in Social Networks• Communication Cost• Challenges in Finding Teams• Approximation Algorithm for Finding Teams• Enumerating Top-k Teams in Polynomial Delay• Finding Teams with Leader• Empirical Results• Conclusion

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CIKM’11 Discovering Top-k Teams of Experts with/without a Leader in Social Networks

Team of Experts

• Given a social network, find top-k teams of experts that can effectively collaborate in order to complete a project.

• Each team might/might not have a leader.

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Team of Experts

• Project: set of required skills

• Expert: an individual with a specific skill-set

• Social Network: represents strength of relationships (the degree of collaboration between any two experts).• For example: LinkedIn, DBLP and …

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Example

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2 1

1

567 6

6 7

Project = {AI, DB, DM, IR}

The numbers on the edge represents how easily two experts can communicate, smallernumbers represents better communication.

8

Are Jack and Thomas Able to Communicate Effectively ?!

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2 1

1

56 7 6

6 7

8

What about Jack, John and Susan?

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2 1

1

567 6

6 7

8

Team of Experts• Team of Expers: Given a set of experts and a project that

requires a set of skills {s1, s2, . . . , sp}, a team of experts is a set of p skill-expert pairs:

{(s1, cs1), (s2, cs2) , . . . , (sp, csp) },

where csk is an expert having skill sk for k = 1, . . . , p.

• A skill-expert pair (sk, csk) means that expert csk is responsible for skill sk in the project.

• How to make sure that the experts can communicate together?

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Communication Cost• For the following team of experts (without a leader)

• The sum of distances of a team of experts is the sum of the shortest distances between the experts responsible for each pair of skills.

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Benefit of Sum of Distances• Previous work in this area defines two communication cost

functions [Lappas et. al]• Diameter of the sub-graph

• The largest shortest path between any two nodes in the sub-graph

• Cost of Minimum Spanning Tree

• The above measures have the following problems:1)They do not consider communication costs between each pair of

skill holders.

2)Instability:a)A slight change in the graph may result in a radical change in the solution.

b)On the other hand, they may be insensitive to adding, deleting and changing a connection in the graph since they only measure part of the communication cost.

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Problem 1

• Team Formation without a Leader : Given a project P and a graph G representing the social

network of a set of experts C, the problem of team formation without a leader is to find a team of experts T for P from G so that the communication cost of T, defined as the sum of distances of T, is minimized.

• What about finding top-k teams of experts? • User might be interested in finding more than one team.

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Challenges• Theorem: Problem 1 is NP-hard.

• Proved in the paper by reduction from 3-satisfiability (3-SAT).

• Solution : Approximation algorithm with guaranteed ratio.

• Total number of teams is exponential regarding the number of required skills.• It is not efficient to generate all teams and then sort them.

• Solution : Enumerating teams in polynomial delay.

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Finding Best Approximate Team (without Leader)

• Step 1: for all experts (skill holders) n, for all required skills ki, find the closest node which contains ki.

• Step 2: for all experts n, for all required skills ki, calculate the sum of distances from n to the holder of ki.

• Step 3: Find the expert with the minimum sum of distances among other experts.

• Step 4: Return the set of experts with the minimum sum of distances.

• The approximation ratio of the algorithm is equal to 2.• The weight of the answer is at most twice of the weight of the optimal

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Enumerating in Approximate Order• The Lawler’s technique is used for finding the top-k teams.• In each iteration, the next team is generated by finding the

top team under constraints.• Two problems should be solved

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1- What are the constraints?

2- How top answer can be found efficiently under the constraints?

System Overview

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Required Skills

+Value of k

Find best Team with

no Constraint

Insert the best team with the

search space in priority queue

Fetch the best team from

priority queue and print it

Divide the related search space of the top answer

into sub-spaces

Find best team in each sub-space with associated

constrains

Insert each answer with the related

search space into priority queue

Top-k already printedOR

Empty priority queue

?YESTerminate

NO

Constraints and Search Space

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• Let’s do it using an example !

• Suppose that the required skills are {k1, k2, k3, k4}.

• Ci = {set of experts that holds skill ki }.

• The search space that contains the best team can be represented as {C1 ᵡ C2 ᵡ C3 ᵡ C4}.

• Assume that the best team is (v1, v2, v3, v4), where vi is an expert containing skill ki .

The whole search space

Team of Experts with a Leader• A project often has a leader who is

responsible for monitoring and coordinating the project

• Each expert in the team needs to communicate with the leader to report the progress and discuss issues related to the project.

• The communication cost of the team heavily depends on the distance between the leader and each of the project members.

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Communication Cost• For the following team of experts (with a leader)

• assume that team has a leader L, where L is an expert in the social network which may or may not belong to the team.

• The leader distance of a team of experts is the sum of the shortest distances between its leader and the expert for each required skill.

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Problem 2

• Team Formation with a Leader : Given a project P and a graph G representing the social

network of a set of experts C, the problem of team formation with a leader is to find a team of experts T and an expert L from C as the leader of the team so that the communication cost, defined as the leader distance is minimized.

• This problem can be solved in polynomial time.

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Finding Best Team (with Leader)

• Step 1: for all individuals i, for all required skills ki, find the closest expert to i which contains ki.

• Step 2: for all individuals i (leader candidates), for all required skills ki, calculate the leader distance from i to the holder of ki.

• Step 3: Find the individual (leader) with the minimum leader distance among other individuals.

• Step 4: Return the leader with the set of experts which has the minimum leader distance.

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Experimental Results• The proposed algorithms in this work (Best-SumDistance

and Best-Leader) are compared with the following methods.• Rarest-First, minimizing diameter• Enhanced-Steiner, minimizing the cost of minimum spanning tree

• Two datasets are used: DBLP and IMDb.• DBLP contains 5,658 experts and 8,588 edges.• IMDb contains 6,784 experts and 35,875 edges.

• For the purpose of comparison, exact answers of NP-hard problems are achieved by exhaustive search.

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Communication Cost

DBLP Dataset22/28


Communication Cost

IMDb Dataset23/28


Other Quality Measures Approximation Algorithms

DBLP Dataset24/28


Other Quality Measures Exact Algorithms

DBLP Dataset25/28


Scalability


26/28DBLP Dataset

Conclusion• Two problems are defined:• Finding top-k teams of experts with a leader.• Finding top-k teams of experts without a leader.• An approximation algorithm for finding a team of experts

without a leader with bounded guarantee has been proposed.

• An exact polynomial algorithm for finding a team of experts with a leader has been proposed.

• A procedure of finding top-k teams of experts with polynomial delay is introduced.

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Check the System athttp://graph.cse.yorku.ca:8080/team

It is accepted as a demo paper in ICDM’11

mehdi kargar aijun an york university, toronto, canada discovering top-k teams of experts...

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