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

Morteza Zihayat
Mehdi Kargar
Aijun 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
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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.
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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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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.
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 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.
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Personnel Cost
• 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
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Expertise Cost
• Where is the expertise cost with respect to the skill
and is reversely proportional to the expertise level of the
expert.
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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
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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.
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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’)
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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
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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.
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Finding Supported Efficient Teams
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Phase 2: Finding non-supported efficient teams
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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
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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
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Results of the two phase method in comparison with other
methods on the DBLP graph.
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RESULTS OF ALGORITHMS FOR FINDING
PARETO FRONT
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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.
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Thank You

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

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