On the max min vertex cover problem

Abstract

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−12 approximation ratio, while showing that unless P=NP, the problem is inapproximable within ratio nε−(12) for any strictly positive ε. We also analyze the problem on various restricted classes of graphs, on which we show polynomiality or constant-approximability of the problem. Finally, we show that the problem is fixed-parameter tractable with respect to the size of an optimal solution, to treewidth and to the size of a maximum matching.