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Newton's method for fractional combinatorial optimization
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
The Computational Complexity of Link Building
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On the α-Sensitivity of Nash Equilibria in PageRank-Based Network Reputation Games
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Pagerank optimization in polynomial time by stochastic shortest path reformulation
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
A constant-factor approximation algorithm for the link building problem
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Maximizing pagerank with new backlinks
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J. Hopcroft and D. Sheldon originally introduced network reputation games to investigate the self-interested behavior of web authors who want to maximize their PageRank on a directed web graph by choosing their outlinks in a game theoretic manner. They give best response strategies for each player and characterize properties of web graphs which are Nash equilibria. In this paper we consider three different models for PageRank games on undirected graphs such as certain social networks. In undirected graphs players may delete links at will, but typically cannot add links without the other player's permission. In the deletion-model players are free to delete any of their bidirectional links but may not add links. We study the problem of determining whether the given graph represents a Nash equilibrium or not in this model. We give an O(n^2) time algorithm for a tree, and a parametric O(2^kn^4) time algorithm for general graphs, where k is the maximum vertex degree in any biconnected component of the graph. In the request-delete-model players are free to delete any bidirectional links and add any directed links, since these additions can be done unilaterally and can be viewed as requests for bidirected links. For this model we give an O(n^3) time algorithm for verifying Nash equilibria in trees. Finally, in the add-delete-model we allow a node to make arbitrary deletions and the addition of a single bidirectional link if it would increase the page rank of the other player also. In this model we give a parametric algorithm for verifying Nash equilibria in general graphs and characterize so called @a-insensitive Nash Equilibria. We also give a result showing a large class of graphs where there is an edge addition that causes the PageRank of both of its endpoints to increase, suggesting convergence towards complete subgraphs.