Solving the Replacement Paths Problem for Planar Directed Graphs in O(nlog n) Time
Christian Wulff‐Nilsen · 2009
In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s toavertext. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time bound was O(n log 2 n). 1