… of shortest paths. For an ordered pair (s,t) of vertices, we define their shortest paths graph
forumla to be a directed graph on V, which consists of all edges that reside on a shortest path …

… a graph has an ideal orientation. … orientation of a graph G = (V, E) with positive edge
lengths with respect to two given pairs of vertices (i, i’), (j, j’), or conclude that no such orientation …

… a shortest path between s 1 and t 1 . Robbins [12] showed that every 2-edge-connected
graph can … Therefore, a graph G has at least one orientation for any set of st-pairs if G is 2-edge-…

… At any point in time, we will be holding a partial orientation G ℓ of G and a subset of
shortest paths, where these sets are indexed according to the step number that has just been …

… graph theory and network optimization is that of computing a \shortest path" between two
nodes, s and t, in a graph … (position-orientation pair) to a goal location (no orientation speci ed), …

… Given an undirected graph G and k pairs of vertices (~1, tl ), . … an orientation G’ of G such
that the length of the shortest path … orientation G’ of G such that the length of the shortest path …

… At any point in time, we will be holding a partial orientation Gl of G and a subset Pl ⊆ P of
shortest paths, where these sets are indexed according to the step number that has just been …

… a graph orientation problem that can be viewed as a generalization of Minimum Graph …
In this paper, we study a graph orientation problem that can be viewed as a generalization …

… that every undirected graph G admits an orientation H with the … bridgeless graph of radius I’
admits an orientation of radius at … to u is the number of edges in a shortest path (resp. directed …

… 1.3 Related work Ripphausen-Lipa, Wagner, and Weihe [14, 19] have given algorithms for
flow problems in planar graphs using an approach that considers orientation and crossing …