How do you determine NP completeness of a problem?
Suppose X is solvable in polytime, and let Y be any problem in NP. We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete.
Is weighted vertex cover NP complete?
Therefore it is a valid polynomial time reduction. So, we can solve vertex cover problem in polynomial time which is a contradiction. Hence subset sum problem is NP complete.
Is clique and set cover problem NP complete?
This operation can be done in polynomial time. Since VERTEX-COVER can be reduced to CLIQUE in polynomial time, CLIQUE ∈ NP and VERTEX-COVER is NP-Complete, CLIQUE is also NP-Complete.
Which of the given problems are NP complete node cover problems?
1. Which of the given problems are NP-complete? Explanation: Vertex cover or Node cover problem, and Hamilton Circuit problem, both are NP complete type of problems.
Is vertex cover a problem with NP?
Its decision version, the vertex cover problem, was one of Karp’s 21 NP-complete problems and is therefore a classical NP-complete problem in computational complexity theory.
What is NP complete problems?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
What is N and P NP-complete problems?
P is a set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. NP-complete problems are the hardest problems in the NP set.
How to prove that the vertex cover is NP complete?
VC is Non-deterministic Polynomial (NP). A NPC problem can be reduced into VC. To prove VC is NP, find a verifier which is a subset of vertices which is VC and that can be verified in polynomial time. For a graph of n vertices it can be proved in O (n2). Thus, VC is NP.
Is there polynomial time solution to vertex cover problem?
The following are some examples. Vertex Cover Problem is a known NP Complete problem, i.e., there is no polynomial-time solution for this unless P = NP. There are approximate polynomial-time algorithms to solve the problem though. Following is a simple approximate algorithm adapted from CLRS book.
Which is an example of the vertex cover problem?
First let us understand the notion of an instance of a problem. An instance of a problem is nothing but an input to the given problem. An instance of the Vertex Cover problem is a graph G (V, E) and a positive integer k, and the problem is to check whether a vertex cover of size at most k exists in G.
What is the vertex cover of an undirected graph?
A vertex cover of an undirected graph is a subset of its vertices such that for every edge (u, v) of the graph, either ‘u’ or ‘v’ is in the vertex cover. Although the name is Vertex Cover, the set covers all edges of the given graph.