Non-crossing Shortest Paths in Undirected Unweighted Planar Graphs in Linear Time

Lorenzo Balzotti, Paolo Giulio Franciosa

Abstract: Given a set of terminal pairs on the external face of an undirected unweighted planar graph, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, if such paths exist. This allows us to compute distances between each terminal pair, within the same time bound.