Is vertex cover NP-complete?
Thus, vertex cover is NP Hard. Since vertex cover is in both NP and NP Hard classes, it is NP Complete.
Is edge cover NP-complete?
Computing total edge covers. We now consider the t-Total Edge Cover problem. For this problem becomes the Edge Cover problem, which has long been known to be solvable in polynomial time [8]. The problem is NP-complete for each fixed 2 ≤ t ≤ k [9, Theorem 3].
Is clique and set cover NP-complete?
Since VERTEX-COVER can be reduced to CLIQUE in polynomial time, CLIQUE ∈ NP and VERTEX-COVER is NP-Complete, CLIQUE is also NP-Complete.
What is K in vertex cover?
k-Vertex Cover: Given a graph G=(V,E) where V is a set of vertices and E a set of edges, and an integer k, the k-Vertex Cover problem determines if there exists a subset of vertices V′ of V of size at most k, such that every edge of E has at least one vertex in V′.
Is TSP NP-hard?
In fact, TSP belongs to the class of combinatorial optimization problems known as NP-complete. This means that TSP is classified as NP-hard because it has no “quick” solution and the complexity of calculating the best route will increase when you add more destinations to the problem.
Is Hamiltonian cycle NP-complete?
Conclusion: Since, the Hamiltonian Cycle is both, a NP-Problem and NP-Hard. Therefore, it is a NP-Complete problem.
Why Is Set cover NP-complete?
Theorem: Set Cover is NP-Complete. Proof: First, we argue that Set Cover is in NP, since given a collection of sets C, a certifier can efficiently check that C indeed contains at most k elements, and that the union of all sets listed in C does include all elements from the ground set U.
Is traveling salesman NP-complete?
What is the maximum vertex cover?
In Maximum k-Vertex Cover (Max k-VC), the input is an edge-weighted graph G and an integer k, and the goal is to find a subset S of k vertices that maximizes the total weight of edges covered by S. Here we say that an edge is covered by S iff at least one of its endpoints lies in S.
What is the minimum size of a vertex cover?
The size of the minimum vertex cover is 1 (by taking either of the endpoints). 3. Star: |V | − 1 vertices, each of degree 1, connected to a central node. The size of the minimum vertex cover is k − 1 (by taking any less vertices we would miss an edge between the remaining vertices).
Is travel salesman NP a problem?
Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).
Why is TSP so hard?