What is vertex cover approximation?

Given a G = (V,E), find a minimum subset C ⊆ V , such that C “covers” all edges in E, i.e., every edge ∈ E is incident to at least one vertex in C. Figure 1: An instance of Vertex Cover problem. An optimal vertex cover is {b, c, e, i, g}. As it turns out, this is the best approximation algorithm known for vertex cover.

Is vertex cover in P?

Since vertex cover is in both NP and NP Hard classes, it is NP Complete.

Is vertex cover solvable?

Since the vertex cover problem is known to be solvable in time polynomial in n on bipartite graphs, our result is, to the best of our knowledge, the first example of a problem solvable in polynomial time whose reconfiguration version is W[1]-hard.

What is the size of 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).

How do I verify my vertex cover?

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. Now consider the “clique” problem which is NPC and reduce it into VC to prove NPC.

What is vertex cover problem in algorithm?

The vertex cover problem is an NP-Complete problem, which means that there is no known polynomial-time solution for finding the minimum vertex cover of a graph unless it can be proven that P = NP. There, however, exists polynomial-time approximate algorithms to find the vertex cover of a graph.

Is there a vertex cover of size k?

In particular, if the algorithm picked k edges, the vertex cover found has size 2k. But, any vertex cover must have size at least k since it needs to have at least one endpoint of each of these edges, and since these edges don’t touch, these are k different vertices.

How do you solve vertex cover problems?

A simple approximate algorithm for the vertex cover problem is described below:

  1. Initialize the vertex cover set as empty.
  2. Let the set of all edges in the graph be called E.
  3. While E is not empty:
  4. Return the final obtained vertex cover set, after the set E is empty.

Is vertex cover a NP?

The vertex cover problem is an NP-complete problem: it was one of Karp’s 21 NP-complete problems.

https://www.youtube.com/watch?v=D2l_kYxhjs0