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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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We have considered, in the context of a randomized algorithm for 2SAT, a random walk with a completely reflecting boundary at 0—that is, whenever position 0 is reached, with probability 1 we move to position 1 at the next turn. Consider now a random walk with a partially reflecting boundary at 0– whenever position 0 is reached, with probability 1/4 we move to position 1 at the next turn, and with probability 3/4 we stay at 0. Everywhere else the random walk either moves up or down 1, each with probability 1/2. Find the expected number of moves to reach n starting from position i using a random walk with a partially reflecting boundary. (You may assume there is a unique solution to this problem, as a function of n and i; you should prove that your solution satisfies the appropriate recurrence.)

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