GATE CS 2014 Set 3 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumP, NP, NP-CompleteComplexity TheoryAlgorithmsPolynomial Reductions
Algorithms → Complexity Theory → P, NP, NP-Complete
Last updated
Question
Consider the decision problem 2CNFSAT defined as follows:For example, is a Boolean formula and it is in 2CNFSAT.The decision problem 2CNFSAT is
Correct answer
(B) solvable in polynomial time by reduction to directed graph reachability.
Solution
2-SAT (or 2CNFSAT) is the problem of determining if a boolean formula in 2-CNF is satisfiable. It is known to be in P (Polynomial Time).The standard algorithm to solve 2-SAT involves constructing an implication graph where each clause is represented as two directed edges: and . The formula is unsatisfiable if and only if there exists a variable such that there is a path from to and a path from to in this graph (i.e., they belong to the same Strongly Connected Component).This reduces the problem to finding strong connected components or checking reachability in a directed graph, which can be done in linear time .Thus, it is solvable in polynomial time by reduction to directed graph reachability.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Complexity Theory
2026 Set 1 Q17Consider the following recurrence relations: For all ,…2026 Set 2 Q24Consider the following functions, where is a positive integer.…2026 Set 2 Q25Which of the following can be recurrence relation(s) corresponding to an algorithm with time…2026 Set 2 Q32Consider an array . Suppose the merge sort algorithm is…2026 Set 2 Q37Let be a weighted directed acyclic graph with edges and vertices. Given and a…