1
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the decision problem 2CNFSAT defined as follows:

{ $$\Phi $$ | $$\Phi $$ is a satisfiable propositional formula in CNF with at most two literal per clause}

For example, $$\Phi = \left( {{x_1} \vee {x_2}} \right) \wedge \left( {{x_1} \vee {{\overline x }_3}} \right) \wedge \left( {{x_2} \vee {x_4}} \right)$$ is a Boolean formula and it is in 2CNFSAT.

The decision problem 2CNFSAT is

A
NP-Complete.
B
Solvable in polynomial time by reduction to directed graph reachability.
C
Solvable in constant time since any input instance is satisfiable.
D
NP-Hard, but not NP-complete.
2
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?
A
GATE CSE 2014 Set 1 Algorithms - P and NP Concepts Question 3 English Option 1
B
GATE CSE 2014 Set 1 Algorithms - P and NP Concepts Question 3 English Option 2
C
GATE CSE 2014 Set 1 Algorithms - P and NP Concepts Question 3 English Option 3
D
GATE CSE 2014 Set 1 Algorithms - P and NP Concepts Question 3 English Option 4
3
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
The subset-sum problem is defined as follows:
Given a set S of n positive integers and a positive integer W, determine whether there is a subset of S Whose elements sum to W. An algorithm Q solves this problem in O(nW) time. Which of the following statements is false?
A
Q solves the subset-sum problem in polynomial time when the input is encoded in unary
B
Q solves the subset-sum problem in polynomial time when the input is encoded in binary
C
The subset sum problem belongs to the class NP
D
The subset sum problem is NP-hard
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V, E) with |V| divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?
A
Both DHAM3 and SHAM3 are NP-hard
B
SHAM3 is NP-hard, but DHAM3 is not
C
DHAM3 is NP-hard, but SHAM3 is not
D
Neither DHAM3 nor SHAM3 is NP-hard
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