Database Management System

Which of the following is used for indexing in database systems?
(i) Transaction log
(ii) B-tree
(iii) Views
(iv) Triggers

A B-tree of order 4 and of height 3 will have a maximum of ____ keys.
(i) 255
(ii) 63
(iii) 127
(iv) 188

Compared with B-tree indexing, hashing is preferred when queries mainly involve:

(i) Range searches
(ii) Ordered traversal
(iii) Exact match search
(iv) Sorting

For a B-tree of order m, every non-root internal node must have at least:

(i) m/2 children
(ii) [m/2] children
(iii) [m/2]-1 children
(iv) m-1 children

Construct the B+ tree for the following set of key values:
(2, 3, 5, 7, 11, 17, 19, 23, 29, 31)
Assume that tree is initially empty and values are added in ascending order. Construct B+ tree for the cases where the number of pointers that will fit in one node is as follows:
(a) Four
(b) Six
(c) Eight

Explain different indexing techniques used in databases.

What are indices in database systems? Explain the need and advantages of indexing. Describe various types of indexing techniques including primary index, secondary index, clustered and non-clustered indexes with the help of suitable diagrams.

Consider a hash table of size 10 with the hash function $h(k) = k \pmod{10}$. Insert the keys 23, 43, 13, 27, 37, and 50 into the hash table. Construct the hash table using separate chaining for collision resolution and then reconstruct it using linear probing. Compare the final arrangements obtained using both methods.

What is a B-tree? Explain its structure, order, and properties. How is a B-tree used in database indexing? Demonstrate insertion and search operations in a B-tree with a proper example. Also compare B-tree with binary search tree in context of database performance.

For the following set of key values construct a B+ tree with a degree 4:
5, 10, 15, 29, 35, 46, 58, 63, 67, 89
Initially tree is empty. Values must be added in ascending order. Show the step-by-step construction.

What is multilevel indexing? Explain in detail.