Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality

Tomasz P. Michalak , Karthik .V. Aadithya , Piotr Lech Szczepański , Balaraman Ravindran , Nicholas R. Jennings

Abstract

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics)and demonstrate that they deliver significant speedups over the Monte Carlo approach. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.
Author Tomasz P. Michalak
Tomasz P. Michalak,,
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, Karthik .V. Aadithya
Karthik .V. Aadithya,,
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, Piotr Lech Szczepański (FEIT / IN)
Piotr Lech Szczepański,,
- The Institute of Computer Science
, Balaraman Ravindran
Balaraman Ravindran,,
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, Nicholas R. Jennings
Nicholas R. Jennings,,
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Journal seriesJournal of Artificial Intelligence Research, ISSN 1076-9757
Issue year2013
Vol46
Pages607-650
ASJC Classification1702 Artificial Intelligence
DOIDOI:10.1613/jair.3806
URL http://www.jair.org/vol/vol46.html
ProjectDevelopment of new methods and algorithms in the following areas: computer graphics, artificial intelligence, and information systems, and distributed systems . Project leader: Rybiński Henryk, , Phone: +48 22 234 7731, start date 29-05-2012, planned end date 31-12-2012, end date 30-11-2013, II/2012/DS/1, Completed
WEiTI Działalność statutowa
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 25.0, 02-02-2020, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 02-02-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2013 = 2.873; WoS Impact Factor: 2013 = 0.904 (2) - 2013=1.685 (5)
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