GATE CSE 2006 | P and NP Concepts Question 8 | Algorithms

GATE CSE 2006

MCQ (Single Correct Answer)

-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?

Both DHAM₃ and SHAM₃ are NP-hard

SHAM₃ is NP-hard, but DHAM₃ is not

DHAM₃ is NP-hard, but SHAM₃ is not

Neither DHAM₃ nor SHAM₃ is NP-hard

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Consider three decision problems P₁, P₂ and P₃. It is known that P₁ is decidable and P₂ is undecidable. Which one of the following is TRUE?

P₃ is decidable if P₁ is reducible to P₃

P₃ is undecidable if P₃ is reducible to P₂

P₃ is undecidable if P₂ is reducible to P₃

P₃ is decidable if P₃ is reducible to P₂ 's complement

GATE CSE 1992

MCQ (Single Correct Answer)

-0.6

Which of the following problems is not NP-hard?

Hamiltonian circuit problem

The 0/1 Knapsack problem

Finding bi-connected components of a graph

The graph coloring problem

GATE CSE Subjects

Theory of Computation

Finite Automata and Regular Language Push Down Automata and Context Free Language Undecidability Recursively Enumerable Language and Turing Machine

Operating Systems

Process Concepts and Cpu Scheduling Synchronization and Concurrency Deadlocks Memory Management File System IO and Protection

Algorithms

Complexity Analysis and Asymptotic Notations Searching and Sorting Divide and Conquer Method Greedy Method Dynamic Programming P and NP Concepts

Digital Logic

Number Systems Boolean Algebra K Maps Combinational Circuits Sequential Circuits

Database Management System

Er Diagrams Functional Dependencies and Normalization Structured Query Language Relational Algebra Transactions and Concurrency File Structures and Indexing

Data Structures

Arrays Stacks and Queues Linked List Trees Graphs Hashing

Computer Networks

Concepts of Layering Data Link Layer and Switching Network Layer Application Layer Protocol Routing Algorithm TCP UDP Sockets and Congestion Control Lan Technologies and Wi-Fi Network Security

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Discrete Mathematics

Set Theory & Algebra Linear Algebra Graph Theory Combinatorics Mathematical Logic Probability Calculus

Programming Languages

Basic of Programming Language Function and Recursion Pointer and Structure in C

Computer Organization

Computer Arithmetic Pipelining Machine Instructions and Addressing Modes Memory Interfacing IO Interface Alu Data Path and Control Unit Secondary Memory