On the complexity of cooperative solution concepts
Mathematics of Operations Research
Complexity of the minimum base game on matroids
Mathematics of Operations Research
Fast approximation of centrality
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Introduction to algorithms
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
A randomized method for the shapley value for the voting game
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
A linear approximation method for the Shapley value
Artificial Intelligence
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Power and stability in connectivity games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Determining the top-k nodes in social networks using the Shapley value
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
Polynomial calculation of the Shapley value based on sampling
Computers and Operations Research
Power in threshold network flow games
Autonomous Agents and Multi-Agent Systems
Power Indices in Spanning Connectivity Games
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
On the computational complexity of coalitional resource games
Artificial Intelligence
On the complexity of compact coalitional games
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Learning influence probabilities in social networks
Proceedings of the third ACM international conference on Web search and data mining
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
A logic-based representation for coalitional games with externalities
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Representation of coalitional games with algebraic decision diagrams
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Computational Aspects of Cooperative Game Theory (Synthesis Lectures on Artificial Inetlligence and Machine Learning)
PRIMA'11 Proceedings of the 14th international conference on Agents in Principle, Agents in Practice
QUBE: a quick algorithm for updating betweenness centrality
Proceedings of the 21st international conference on World Wide Web
A new approach to betweenness centrality based on the Shapley Value
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
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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.