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Which of the following statements are TRUE?

  1. The problem of determining whether there exists a cycle in an undirected graph is in P.
  2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
  3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.

(A) 1, 2 and 3     (B) 1 and 2 only     (C) 2 and 3 only     (D) 1 and 3 only

asked in Theory of Computation by Veteran (346k points)
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1 Answer

+18 votes
Best answer

Cycle detection is graph is in P as it can be done using a graph traversal (O(V+E))

Ref: http://www.geeksforgeeks.org/detect-cycle-undirected-graph/

If a problem is in P then it is also in NP as P is a subset of NP. So, both 1 and 2 are TRUE. 

Statement 3 is also true as NP-Complete requires a problem to be in NP and for any problem in NP, we have a non-deterministic polynomial time algorithm. 

So, answer is A- 1, 2 and 3 are TRUE.  

answered by Veteran (346k points)
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Is problem solved by NON-deterministic polynomial time algorithm  is same as saying that there is Non-deterministic Turing machine which solve in polynomial time?

 the formal definition of NP is the set of decision problems solvable in polynomial time by a theoretical non-deterministic Turing machine. This second definition is the basis for the abbreviation NP, which stands for "nondeterministic,polynomial time."

 

Yes, more precisely non deterministic halting TM I guess.
Answer:

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