, if the number of doubly oriented edges of a feasible orientation Gi is strictly less than that of Gres then Gres := Gi Orient(s?, t ? , +, Gi) : orientation of Gi[s?, t ? ] + form s? towards t ? Orient(s?, Gi) : orientation of Gi[s?
, P ) be the set of pairs (s, t) s.t. there is in G exactly one (resp. two) path(s) from s to t
, If |C | = k, then we add to |C | a convenient number of arbitrarily sets from C to ensure that |C | = k (C remains a set cover of C)
, Again, we use the previous reduction (proof of Theorem 10), but we consider the variant MINIMUM SET COVER-2 of the MINIMUM SET COVER problem in which each X j ? X appears in exactly two sets in C. For each pair of vertices (s i , s i ) ? P there is a unique path in G, from s i to s i (that is the edge (s i , s i )
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