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

Undecidability Finite Automata and Regular Language Push Down Automata and Context Free Language 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

K Maps Boolean Algebra Combinational Circuits Number Systems Sequential Circuits

Database Management System

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

Data Structures

Trees Hashing Arrays Linked List Graphs Stacks and Queues

Computer Networks

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

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

Discrete Mathematics

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

Programming Languages

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

Computer Organization

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