A note on line broadcast in digraphs under the edge-disjoint paths mode Original Research Article

It is known that unless NP⊂DTIME(nlog log n), no polynomial-time approximation algorithm for the multicast problem can have approximation ratio less than Ω(log n) in n-node digraphs under the edge-disjoint paths mode of the line model. In this note, we give a polynomial-time O((Δmin+log n)/(log(Δmin+log n)))-approximation algorithm, where Δmin is the smallest integer k such that there exists a rooted directed tree of maximum out-degree k, spanning the considered digraph.