Chapter 21, Problem 2PE

Explanation of Solution

a.

Load-balanced range partitioning function:

When partitioning data over $\text{n}$ disks, range partitioning distributes the records by assigning adjacent attribute-value ranges-each disk.

• Consider the user has a histogram where values are between 1 and 100

Explanation of Solution

b.

Algorithm:

The algorithm for computing a balanced range partition will be as follows:

• Let the partitions be ${\text{p}}_{\text{1}}{\text{, p}}_{\text{2}}{\text{, p}}_{\text{3}}\text{,…}{\text{.p}}_{\text{p}}$ and the histogram range be ${\text{h}}_{\text{1}}{\text{, h}}_{\text{2}}{\text{, h}}_{\text{3}}{\text{,…h}}_{\text{h}}$, and the frequencies of the histogram range be ${\text{n}}_{\text{1}}{\text{, n}}_{\text{2}}{\text{, n}}_{\text{3}}\text{,…}{\text{.n}}_{\text{n}}$.
• Each partition consists of $\text{N/P}$ records, so that $\text{N=}{\displaystyle {\sum }_{\text{i=1}}^{\text{k}}\left({\text{n}}_{\text{i}}\right)}$
• Construct the balanced partitioning sector,
  • Establish the value of  ${\text{k}}_{\text{1}}{}^{\text{th}}$  record, such that ${\text{k}}_{\text{1}}\text{=N/P}$ .
  • Establish the value of  ${\text{k}}_{\text{2}}{}^{\text{th}}$  record, such that ${\text{k}}_{\text{2}}\text{=2 xN/P}$.
  • And so on till the value of ${\text{k}}_{\text{p-1}}{}^{\text{th}}$ record, such that ${\text{k}}_{\text{p-1}}\text{=}\left(\text{p-1}\right)\text{xN/P}$