1.a. Explain different Distance measures for Big Data.

1.b Explain the Hadoop Architecture with its features.

1.c Explain CAP Theorem? how it is different from ACID Properties.

1.d What are the shortcomings of nearest neighbour technique in collaborative filtering method? Suggest some improvements.

2.a Write a Map-Reduce Algorithm for Binary search tree. Explain the flow of execution.

2.b Suppose a stream consists of the integers 2,1,6,1,5,9,2,3,5. Let the hash functions all be of the from h(x)=ax+b mod 16 for some a & b. You should treat the results as a 4 bit binary integer. Determine the tail length for each stream element and the resulting estimate of the number of distinct elements if the hash function is:
a) h(x) = 2x+3 mod 16
b) h(x) = 4x+1 mod 16
c) 5x mod 16

3.a Explain Different types of recommendation system with real time examples.

3.b Consider the portion of a Web graph as shown in Figure-1 i) Compute the hub and authorities scores for all nodes.
ii) Does this graph contain spider traps? Dead ends? If so, which nodes.

4.a.i. Write a short note on PCY Algorithm

4.a.ii. Write a short note on CURE algorithm

4.b Imagine there are 100 baskets, numbered 1,2,....,100 items, similarity numbered. Item 1 is in basket J if and only if I divides J evenly. For example basket is 24 is the set of items {1,2,3,4,6,8,12,24}. Describe all the association rules that have 100% confidence.

5.a Define Bloom Filter. Explain the concept of Bloom filter. Algorithm with example.

5.b Explain HITS algorithm with example.

6.a NoSQL architectural pattern with example.

6.b Matrix Multiplication by Map Reduce

6.c List & explain Big data:- 1) Characteristics 2) Types 3) Challenges