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SIAM Journal on Computing
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Stochastic models for the Web graph
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Multiway cuts in node weighted graphs
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Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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When selfish meets evil: byzantine players in a virus inoculation game
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Inoculation strategies for victims of viruses and the sum-of-squares partition problem
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Altruism, selfishness, and spite in traffic routing
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On the windfall of friendship: inoculation strategies on social networks
Proceedings of the 9th ACM conference on Electronic commerce
Social and Economic Networks
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ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Toward optimal vaccination strategies for probabilistic models
Proceedings of the 20th international conference companion on World wide web
Controlling infection by blocking nodes and links simultaneously
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
The robust price of anarchy of altruistic games
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
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A derandomized approximation algorithm for the critical node detection problem
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On the Windfall and price of friendship: Inoculation strategies on social networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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In this paper, we study the vaccination of graphs against the outbreak of infectious diseases, in the following natural model generalizing a model by Aspnes et al.: An infectious disease breaks out at a random node of the graph and propagates along the edges of the graph. Vaccinated nodes cannot be infected, nor pass on the infection, whereas all other nodes do. The decisions on which nodes get vaccinated must be made before the random outbreak location is known. There is a cost associated with vaccination and a different cost with getting infected. In this model, we provide two results. First, we improve the approximation guarantee for finding the best vaccination strategy from O(log1.5 n) to O(log z) (where z is the support size of the outbreak distribution), by rounding a natural linear program with region-growing techniques. Second, we analyze the impact of autonomy on the part of the nodes: while a benevolent authority may suggest which nodes should be vaccinated, nodes may opt out after being chosen. We analyze the "Price of Opting Out" in this sense under partially altruistic behavior. Individuals base their decisions on their own cost and the societal cost, the latter scaled by some factor ß. If the altruism parameter is ß=0, it is known that the Price of Anarchy and Price of Stability can be Θ(n). We show that with positive altruism, Nash Equilibria may not exist, but the Price of Opting Out is at most 1/ß (whereas the Price of Anarchy can remain at Θ(n)).