國立雲林科技大學
National Yunlin University of Science and Technology
Finding a Team of Experts in
Social Networks
Theodoros Lappas, Kun Liu, and Evimaria Terzi
KDD, 2009
Reported by Wen-Chung Liao, 2009/12/22
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Outlines
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Motivation
Objective
Preliminary
Problems
Algorithms
Experiments
Conclusions
Comments
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Motivation
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The success of a project depends not only on
the expertise of the people who are involved,
but also on how effectively they collaborate,
communicate and work together as a team.
Figure 1: Network of connections
between individuals in
{a, b, c, d, e}.
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Xa={algorithms},
Xb={web programming},
Xc={software engineering, distributed systems},
Xd={software engineering}
Xe={software engineering, distributed systems,
web programming}.
T={algorithms, software engineering, distributed
systems, web programming}.
X’ = {a, b, c} or X” = {a, e}
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Objectives
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Given a task T that requires a set of skills, our
goal is to find a set of individuals X’ X, such
that every required skill in T is exhibited by at
least one individual in X’.
Additionally, the members of team X’ should
define a subgraph in G with low
communication cost.
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Preliminaries
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X = {1, . . ., n}: n individuals
A = {a1, . . . , am}: a universe
of m skills
Xi A
T: a task, a subset of skills
required to perform a job.
T A.
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S(a): the support set of the
skill a, the set of individuals in
X that has the skill a.
S(a) = {i | i X and a Xi}.
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G(X,E): an undirected and
weighted graph
d(i, i’)
Path(i, i’)
d(i,X’) = mini’ X’ d(i, i’)
Path(i, X’)
G[X’]: the subgraph of G that
contains only the nodes in X’.
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Problems
Problem [Team Formation]:
Given the set of n individuals X = {1, . . . , n}, a graph G(X,E),
and task T, find X’ X, so that C (X’, T) = T, and the
communication cost Cc(X’) is minimized.
Diameter (R): Cc-R(X’)
Minimum Spanning Tree (Mst): Cc-Mst (X’),
Proposition 1. The Diameter-TF problem is NP-complete.
Proposition 2. The Mst-TF problem is NP-complete.
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Algorithms
S(a1)
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2
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S(a0)
={1,7}
S(a2)
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O(|S(arare)| × n)
Proposition 3. Cc-R(X’) ≦2 Cc-R(X*)
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S(a3)
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R1=max{1, 2, 2}=2
R7=max{1, 0, 1}=1
X’= {7}∪{2, 8}
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O(|T| × |X|)
O(|X0| × |E|)
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3 v*
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1
7
v
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X’
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8
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X0
N.Y.U.S.T.
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O(k × |E|)
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Y2
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4
1
7
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Y1
v
X’
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6
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Y3
v*
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Experiments
• GreedyDiameter (GreedyMST)
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DBLP dataset: papers in DB, DM, AI and T conferences.
Xdblp: authors that have at least three papers.
5508 individuals.
Xi: terms that appear in at least two titles of papers that
author i has co-authored.
1792 distinct skills.
Authors i, i’ are connected in Gdblp (Xdblp,E) if they appear
as co-authors in at least two papers.
A task T(t, s) is generated: (1) select S from {DB, DM,
AI,T} with |S| = s. (2) randomly pick t required skills.
For every (s, t), generate 100 random tasks, t=2, 4,… , 20
and s = 1,…,4.
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Experiments
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Conclusion
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Address the problem of forming a team of
skilled individuals to perform a given task,
while minimizing the communication cost
among the members of the team.
Prove that the Team Formation problem is NPHard.
Propose appropriate approximation algorithms.
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Comments
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Advantage
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Shortage
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Applications
─ Team formation
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