cs502 current paper subjective type fall 2010 on 21-02-2011

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1.What are two steps generally involved while developing a dynamic programming algorithm?
i. How Dijkstra’s algorithm operates?
ii. What is the running time of the Dijkstra’s algorithm?


3.Answer yes or no and give a brief explanation for your choice.
If problem A reduces (is polynomial-time reducible) to problem B and B is NP-complete then A is NP-complete

4.The following adjacency matrix represents a graph that consists of four vertices labeled 0, 1, 2 and 3. The entries in the matrix indicate edge weights.

0
1
2
3
0
0
1
0
3
1
2
0
4
0
2
0
1
0
1
3
2
0
0
0
Answer the following question:
Can an adjacency matrix for a directed graph ever not be square in shape? Why or why not?

5. Consider the following two problems. In P1 we are given as input a set of n squares (specified by their corner points), and a number k. The problem is to determine whether there is any point in the plane that is covered by k or more squares.
In P2 we are given as input an n–vertex graph, and a number k; the problem is to determine whether there is a set of k mutually adjacent vertices. (E.g. for k = 3 we are just looking for a triangle in the graph.).
Obviously, the problems are both in NP. There exists a simple translation from P1 to P2: just make a graph vertex for each square, and add an edge between a pair of vertices if the corresponding two squares overlap.
If P1 is NP-complete, would this translation imply that P2 is NP-complete?
(Give your Answer in Yes or No)
What is the application of edit distance technique?
Formally describe Minimum Spanning Trees Problem.

6. Let the adjacency list representation of an undirected graph is given below. Explain what general property of the list indicates that the graph has an isolated vertex.

a à b à c à e
b à a à d
c à a à d à e à f
d à b à c à f
e à a à c à f
f à c à d à e
g

7. What are the minimum and maximum numbers of elements in a heap of height h?

1. Where clique cover problem arises?
2. What is decision problem, also explain with example?
9. Show the strongly connected components of the following graph using DFS algorithm. Take node E as a starting node. [You can show final result in exam software and need not to show all intermediate steps].



Please find the attachments for the diagrams.



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