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
AbstractThe 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.
|Journal series||Journal of Artificial Intelligence Research, ISSN 1076-9757|
|Project||Development 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
|Score|| = 25.0, 02-02-2020, ArticleFromJournal|
= 30.0, 02-02-2020, ArticleFromJournal
|Publication indicators||: 2013 = 2.873; : 2013 = 0.904 (2) - 2013=1.685 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.