Given a directed graph G with non negative cost on the arcs, a directed
tree cover of G is a rooted directed tree such that either head or tail (or
both of them) of every arc in G is touched by T. The minimum directed tree
cover problem (DTCP) is to find a directed tree cover of minimum cost. The
problem is known to be NP-hard. In this paper, we show that the weighted Set
Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to
approximate DTCP with the same ratio as for SCP. We show that this expectation
can be satisfied in some way by designing a purely combinatorial approximation
algorithm for the DTCP and proving that the approximation ratio of the
algorithm is max{2,ln(D+)} with D+ is the maximum outgoing degree of
the nodes in G.Comment: 13 page