On the max min vertex cover problem

On the max min vertex cover Problem

We address the max min vertex cover problem, which is the maximization version of the well studied min independent dominating set problem, known to be NP-hard and highly inapproximable in polynomial time. We present tight approximation results for this problem on general graphs, namely a polynomial approximation algorithm which guarantees an n approximation ratio, while showing that unless P = ...

Results on the min-sum vertex cover problem

Let G be a graph with the vertex set V (G), edge set E(G). A vertex labeling is a bijection f : V (G)→ {1, 2, . . . , |V (G)|}. The weight of e = uv ∈ E(G) is given by g(e) = min{f(u), f(v)}. The min-sum vertex cover (msvc) is a vertex labeling that minimizes the vertex cover number μs(G) = ∑ e∈E(G) g(e). The minimum such sum is called the msvc cost. In this paper, we give both general bounds a...

Efficient Algorithms for the max k -vertex cover Problem

We first devise moderately exponential exact algorithms for max k-vertex cover, with time-complexity exponential in n but with polynomial space-complexity by developing a branch and reduce method based upon the measure-and-conquer technique. We then prove that, there exists an exact algorithm for max k-vertex cover with complexity bounded above by the maximum among c and γ , for some γ < 2, whe...

On approximation of max-vertex-cover

The Limits of Tractability: MIN-VERTEX-COVER

Today, we are talking about the MIN-VERTEX-COVER problem. MIN-VERTEX-COVER is a classic NP-hard optimization problem, and to solve it, we need to compromise. We look at three approaches. First, we consider restricting our attention to a special case: a (binary) tree. Then, we look at an exponential algorithm parameterized by the size of the vertex cover. Finally, we look at approximation algori...