On orientations and shortest paths

Rafael Hassin, Nimrod Megiddo
1989 Linear Algebra and its Applications  
An orientation of an undirected graph is a choice of direction for each of its edges. An orientation is called ideal with respect to a given set of pairs of vertices if it does not increase the shortest-path distances between the members of any of the pairs. A polynomial-time algorithm is given for constructing an ideal orientation with respect to two given pairs and any positive edge-lengths, or else recognizing that no such orientation exists. Moreover, we show that this problem is in the
more » ... s NC. For a general number of pairs the problem is proven NP-complete even with unit edgelengths.
doi:10.1016/0024-3795(89)90481-3 fatcat:w5f54xcluret5e3tekxskfmv4i