Pagerank optimization in polynomial time by stochastic shortest path reformulation

  • Authors:

  • Balázs Csanád Csáji;Raphaël M. Jungers;Vincent D. Blondel

  • Affiliations:

  • Department of Electrical and Electronic Engineering, School of Engineering, The University of Melbourne, Australia and Computer and Automation Research Institute, Hungarian Academy of Sciences, Un ...;Lab. for Information and Decision Systems, Massachusetts Institute of Technology and Department of Mathematical Engineering, Université Catholique de Louvain, Belgium;Department of Mathematical Engineering, Université Catholique de Louvain, Belgium

  • Venue:
  • ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
  • Year:
  • 2010

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Abstract

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of the edges from a set of edges that are under our control. By applying results from Markov decision theory, we show that an optimal solution to this problem can be found in polynomial time. It also indicates that the provided reformulation is well-suited for reinforcement learning algorithms. Finally, we show that, under the slight modification for which we are given mutually exclusive pairs of edges, the problem of PageRank optimization becomes NP-hard.