Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n. a) Derive an "information theoretic" lower bound on M(m,n). b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).

Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n. a) Derive an "information theoretic" lower bound on M(m,n). b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).

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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Question

Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n.

a) Derive an "information theoretic" lower bound on M(m,n).

b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).

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