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August 2001 Random walks with ``back buttons''
Ronald Fagin, Anna R. Karlin, Jon Kleinberg, Prabhakar Raghavan, Sridhar Rajagopalan, Ronitt Rubinfeld, Madhu Sudan, Andrew Tomkins
Ann. Appl. Probab. 11(3): 810-862 (August 2001). DOI: 10.1214/aoap/1015345350

Abstract

We introduce backoff processes, an idealized stochastic model of browsing on the World Wide Web, which incorporates both hyperlink traversals and use of the “back button.” With some probability the next state is generated by a distribution over out-edges from the current state, as in a traditional Markov chain.With the remaining probability, however, the next state is generated by clicking on the back button and returning to the state from which the current state was entered by a “forward step.” Repeated clicks on the back button require access to increasingly distant history. We show that this process has fascinating similarities to and differences from Markov chains. In particular, we prove that, like Markov chains, back-off processes always have a limit distribution, and we give algorithms to compute this distribution. Unlike Markov chains, the limit distribution may depend on the start state.

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Ronald Fagin. Anna R. Karlin. Jon Kleinberg. Prabhakar Raghavan. Sridhar Rajagopalan. Ronitt Rubinfeld. Madhu Sudan. Andrew Tomkins. "Random walks with ``back buttons''." Ann. Appl. Probab. 11 (3) 810 - 862, August 2001. https://doi.org/10.1214/aoap/1015345350

Information

Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1021.60031
MathSciNet: MR1865025
Digital Object Identifier: 10.1214/aoap/1015345350

Subjects:
Primary: 60G20 , 60J10 , 60J22

Keywords: Denumerable Markov chains , limiting distributions , Stochastic processes , worldwide web

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 3 • August 2001
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