two-phase pareto set discovery for team formation in social network

Morteza ZihayatMehdi KargarAijun An

York University, Toronto, Canada

Two-Phase Pareto Set Discovery for Team Formation in Social Network

Overview

• Team Formation in Social Networks• Communication Cost• Personnel Cost• Expertise level• Approximation Algorithm • Empirical Results• Conclusion

WIC’14 Two-Phase Pareto Set Discovery for ...

Team of Experts

• Given a social network, find a team of experts that minimizes the communication cost, the personnel cost and the Expertise cost in order to complete a project.

• Clearly, our problem is a three criteria optimization problem.


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 …


Team of Experts

• Feasible Team of Experts: 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)

• expert csk is responsible for skill sk in the project.


How to make sure that the experts can communicate together?

What about the personnel cost?

How to make sure that the experts are the best experts for the required skills (Expertise cost).

Communication Cost• An experts social network is modeled as an undirected and

weighted graph G.• For the following team of experts regarding graph G

• The sum of distances of a team of experts• The sum of the shortest distances between the experts responsible

for each pair of skills.


Personnel Cost• For the following team of experts regarding graph G

• An expert c is paid k × t(c)• k is the number of skills the expert is responsible for in the project.

• More skills the expert uses → More responsibility or tasks → More money he/she is received


Expertise Cost• For the following team of experts regarding graph G

• Where is the expertise cost with respect to the skill and is reversely proportional to the expertise level of the expert.


Three Objective Team Formation Problem• In three objective optimization problem:

• There does not exist an answer that optimizes all the criteria simultaneously.

• Instead of finding one single answer, we can find a set of teams that are not dominated by others.

• Dominance Relation: Given two feasible teams T and T’, T dominates T’ if and only if CC(T)≤CC(T’), EC(T) ≤ EC(T’) and PC(T) ≤ PC(T’). It is denoted as

• Efficient Team: Team T is efficient (also called Pareto-optimal) for a project P if and only if there does not exist a feasible team T’ for P such that

Efficient Teams Categorization• The efficient teams can be categorized into two main

types:• Supported Efficient Teams: can be obtained by solving the

following weighted sum single-objective problem

• We denote this weighted-sum single objective problem as WeightedSingleObjλ

• Non-supported efficient team. An efficient team that is not an optimal team of any WeightedSingleObjλ problem.

Pareto Front Team Formation Problem

• Given a project P and a graph G representing the network of experts, the Pareto front team formation problem is finding the set of all efficient teams from G for P.

• We present a two-phase method for finding the set of efficient teams in graph for a project.

• Lexicographic Optimal Team: Feasible team T is a lexicographic optimal team with respect to a lexicographic order of objectives (cost1,cost2,cost3) if for any other feasible team T’:• Cost1(T) < Cost1(T’) • Or, Cost1(T) = Cost1(T’) but Cost2(T) < Cost2(T’)• Or, Cost1(T) = Cost1(T’) and Cost2(T) = Cost2(T’) and

Cost3(T) < Cost3(T’)

Overview of algorithm

Finding LOT while Optimizing Communication Cost• Finding the optimal team while minimizing the

communication cost is proved to be NP-hard• We find a LOT with respect to the lexicographic order of

(CC,EC,PC)• Since minimizing the communication cost is NP-hard, this

algorithm finds the best team with 2-approximation

Finding LOT while Optimizing Expertise Level

• We propose a method for finding a LOT with the minimum expertise cost

• This algorithm finds an exact LOT in polynomial time • Its time complexity is O(m2 × n) where m is the number of

experts in G and n is number of required skills for project P.

• The similar algorithm is applied for finding LOT while optimizing Personnel cost. The only difference is using personnel costs instead of expertise costs.

Finding Supported Efficient Teams

Phase 2: Finding non-supported efficient teams

Experimental Results (Setup)• Dataset:

• DBLP:• Contains 5,658 experts and 8,588 edges.• The expertise cost of an expert

• Number of publications of the expert. • The more expertise the expert possesses, and thus the more expensive he/she is


Experimental Results (Setup)

• For each number of skills,

• 50 sets of skills are generated randomly

• Corresponding to 50 random projects.

• The average result for each number of skills is computed

for each algorithm.

• Performance Measure:• Hypervolume, Average Distance, Maximal Distance, Precision, Recall,

Run Time


Results of the first phase

Results of the two phase method in comparison with other methods on the DBLP graph.

RESULTS OF ALGORITHMS FOR FINDING PARETO FRONT

Conclusion• The problem of finding a team of experts in a social network

that minimizes the communication cost, expertise cost and the personnel cost is defined.

• An approximation algorithm with a provable performance bound is proposed to find pareto set.

• The algorithm consists of two main phases: finding supported efficient teams and then uses heuristics to find none-supported efficient teams.



Thank You

two-phase pareto set discovery for team formation in social network

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