Abstract
For a given digraph G=( V, A) and a positive integer k, the k-vertex-connectivity unweighted augmentation problem ( k-VCUAP) for G is to find a minimum set of arcs A′ ( A′⊆( V× V− A)) such that the digraph ( V,A∪ A′) is k-vertex-connected. It is known that the time-complexity of 1-VCUAP for every digraph is θ(| V|+| A|). However, it remains still open whether or not there exist polynomial time algorithms for k-VCUAP's ( k≥2) for digraphs. This paper shows that the time-complexity of k-VCUAP ( k≥2) is θ( k| V|) for every rooted directed tree.
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