Random Walks with “Back Buttons”∗
نویسندگان
چکیده
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, backoff 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. To appear: Annals of Applied Probability ∗Extended abstract appeared in Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pages 484–493, Portland, Oregon, May 2000. †IBM Almaden Research Center, Department K53/B2, 650 Harry Road, San Jose, CA 95120. {fagin,sridhar,tomkins}@almaden.ibm.com. ‡Department of Computer Science, Box 352350, University of Washington, Seattle, WA 98195. [email protected]. §Department of Computer Science, Cornell University, Ithaca, NY 14853. [email protected]. ¶Verity, Inc. 892 Ross Drive, Sunnyvale, CA 94089. [email protected]. This work was done while the author was at IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120. ‖NECI, 4 Independence Way, Princeton, NJ 08540. On leave from Cornell University. [email protected]. ∗∗MIT Laboratory for Computer Science, 545 Technology Square NE43-307, Cambridge, MA 02139. [email protected]. Supported in part by an MIT-NEC Research Initiation Award, a Sloan Foundation Fellowship and NSF Career Award CCR-9875511.
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