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DAA | Approximation Algorithm Vertex Cover

DAA | Approximation Algorithm Vertex Cover with daa tutorial, introduction, Algorithm, Asymptotic Analysis, Control Structure, Recurrence, Master Method, Recursion Tree Method, Sorting Algorithm, Bubble Sort, Selection Sort, Insertion Sort, Binary Search, Merge Sort, Counting Sort, etc.

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Vertex Cover

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. We call such vertex cover an optimal vertex cover C*.

Vertex Cover

An approximate algorithm for vertex cover:

Approx-Vertex-Cover (G = (V, E))
{           
       C = empty-set;
    E'= E;
    While E' is not empty do
      {
    Let (u, v) be any edge in E': (*)
    Add u and v to C;
    Remove from E' all edges incident to
       u or v;
      }
    Return C;
}

The idea is to take an edge (u, v) one by one, put both vertices to C, and remove all the edges incident to u or v. We carry on until all edges have been removed. C is a VC. But how good is C?

Vertex Cover

VC = {b, c, d, e, f, g}

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