Help with Union Bounds + Markov\'s Inequality refer to content from: https://bb.

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Question

Help with Union Bounds + Markov's Inequality

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Exercise 4 (Hard). Modify the above construction to yield a data structure that simultaneously has worst case query time O(lgn/lg lg n), space o(n), erpected construction time O(n) AND ma-1 List (Ali)P 10n, no matter what set S of n elements from Ul that is given as input. Hint: Use the wnion bound in combination with Erercise 3.

Explanation / Answer

A relational database organizes data in tables (or relations). A table is made up of rows and columns. A row is also called a record (or tuple). A column is also called a field (or attribute). A database table is similar to a spreadsheet. However, the relationships that can be created among the tables enable a relational database to efficiently store huge amount of data, and effectively retrieve selected data.

A language called SQL (Structured Query Language) was developed to work with relational databases.

Database Design Objective

A well-designed database shall:

· Eliminate Data Redundancy: the same piece of data shall not be stored in more than one place. This is because duplicate data not only waste storage spaces but also easily lead to inconsistencies.

· Ensure Data Integrity and Accuracy:

· [TODO] more

Relational Database Design Process

Database design is more art than science, as you have to make many decisions. Databases are usually customized to suit a particular application. No two customized applications are alike, and hence, no two database are alike. Guidelines (usually in terms of what not to do instead of what to do) are provided in making these design decision, but the choices ultimately rest on the you - the designer.

Step 1: Define the Purpose of the Database (Requirement Analysis)

Gather the requirements and define the objective of your database, e.g. ...

Drafting out the sample input forms, queries and reports, often helps.

Step 2: Gather Data, Organize in tables and Specify the Primary Keys

Once you have decided on the purpose of the database, gather the data that are needed to be stored in the database. Divide the data into subject-based tables.

Choose one column (or a few columns) as the so-called primary key, which uniquely identify the each of the rows.

Primary Key

In the relational model, a table cannot contain duplicate rows, because that would create ambiguities in retrieval. To ensure uniqueness, each table should have a column (or a set of columns), called primary key, that uniquely identifies every records of the table. For example, an unique number customerID can be used as the primary key for the Customers table; productCode for Products table; isbn forBooks table. A primary key is called a simple key if it is a single column; it is called a composite key if it is made up of several columns.

Most RDBMSs build an index on the primary key to facilitate fast search and retrieval.

The primary key is also used to reference other tables (to be elaborated later).

You have to decide which column(s) is to be used for primary key. The decision may not be straight forward but the primary key shall have these properties:

· The values of primary key shall be unique (i.e., no duplicate value). For example, customerName may not be appropriate to be used as the primary key for the Customers table, as there could be two customers with the same name.

· The primary key shall always have a value. In other words, it shall not contain NULL.