What is set cover problem in DAA?
The set covering problem is a significant NP-hard problem in combinatorial optimization. Given a collection of elements, the set covering problem aims to find the minimum number of sets that incorporate (cover) all of these elements.
Is set cover problem NP-hard?
The set-cover is NP and NP-Hard. Therefore, the set-cover is NP-Complete.
What is the time complexity of set cover?
So, the complexity of this approach should be O(2^n). However, Wikipedia says ‘the complexity of Set Cover Problem is m^n where m is the size of the universe and n is the number of sets in the collection’.
What is set cover in graph?
Set covering is equivalent to the hitting set problem. That is seen by observing that an instance of set covering can be viewed as an arbitrary bipartite graph, with the universe represented by vertices on the left, the sets represented by vertices on the right, and edges representing the inclusion of elements in sets.
What is vertex cover algorithm?
A vertex-cover of an undirected graph G = (V, E) is a subset of vertices V’ ⊆ V such that if edge (u, v) is an edge of G, then either u in V or v in V’ or both.
Is set cover the same as vertex cover?
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.
Is set cover in NP?
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.
Which is the minimum size of a set cover?
The cost of the set-covering is the size of C, which defines as the number of sets it contains, and we want |C| to be minimum. An example of set-covering is shown in Figure 1. In this Figure, the minimum size set cover is C = {T3, T4, T5} and it has the size of 3. Figure 1: An instance (X, F) of set-covering problem.
Is vertex cover a NP?
The minimum vertex cover problem is the optimization problem of finding a smallest vertex cover in a given graph. The vertex cover problem is an NP-complete problem: it was one of Karp’s 21 NP-complete problems. It is often used in computational complexity theory as a starting point for NP-hardness proofs.
Why Is set cover NP?
Why is vertex cover algorithm needed?
A Vertex Cover of a graph G is a set of vertices such that each edge in G is incident to at least one of these vertices. The decision vertex-cover problem was proven NPC. Now, we want to solve the optimal version of the vertex cover problem, i.e., we want to find a minimum size vertex cover of a given graph.
What are the types of approximation algorithms?
Types of approximation algorithms. Fully polynomial-time approximation scheme. Constant factor. Knapsack problem.
Why is vertex cover not set cover?
In the Vertex Cover problem, we need to cover the edges using limited number of vertices. In the Set Cover problem, we need to cover elements of a set using limited number of subsets.
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 vertex-cover algorithm?